UC-NRLF 


SB    271    Iflb 


Easy  Lessons 

*  *r 

in 

EINSTEIN 


EDWIN  E. 
OLOS.SON 


LIBRARY 

OF 


DR.  ALBERT  EINSTEIN  IN  His  STUDY 


Wide   World  Photos. 

AT  BERLIN. 


EASY  LESSONS    IN 
EINSTEIN 


A  DISCUSSION  OF  THE  MORE 
INTELLIGIBLE  FEATURES  OF 
THE  THEORY  OF  RELATIVITY 


BY 

EDWIN  E.   SLOSSON,  M.S.,   PH.D. 

Literary  Editor  of  The  Independent,  Associate  in  the  Columbia  School 

of  Journalism.     Author  of il Great  American  Universities ,*' 

*  *  Major  Prophets  of  To-day, "  "  Six  Major  Prophets,  *  * 

"Creative  Chemistry,"  etc. 


With  an  Article  by  Albert  Einstein 
and  a  Bibliography 


ILLUSTRATED 


NEW  YORK 

HARCOURT,  BRACE  AND  HOWE 
1920 


COPYRIGHT,    1920,   BY 
HARCOURT,    BRACE  AND   HOWK,  INC. 


THE  QUINN  ft  BOOEN  COMPANY 
RAHWAY.  N.  J. 


Deepest  of  all  illusory  Appearcmces,  for  hiding  Won- 
der, as  for  many  other  ends,  are  your  two  grand  funda- 
mental world-enveloping  Appearances,  Space  and  Time. 
— CARLYLE. 

Henceforth  Space  in  itself  and  Time  in  itself  sink 
into  mere  shadows  and  only  a  kind  of  union  of  the  two 
can  be  maintained  as  self -existent. — MINKOWSKI. 


045 


A  PREFATORIAL  DIALOGUE 

(The  Purpose  of  which  is  to  Prevent  the  Prospective 
Reader  from  buying  the  Book  under  False  Pretenses) 

SCENE:  A  street  car  in  uniform  movement  of  trans- 
lation in  any  direction. 
TIME  :    The  present. 

The  Reader  (looking  over  the  top  of  a  morning 
paper) :  Here's  something  queer — a 
whole  page  taken  with  a  new  discovery 
in  physics — "  Eclipse  Observations  Con- 
firm Einstein's  Theory  of  Relativity." 
Anything  about  it  in  your  paper? 

The  rAuthor:  Yes.  Here's  a  cartoon  on  it  by  Mc- 
Cutcheon. 

The  Reader:  Must  be  something  to  it  then.  Mc- 
Cutcheon  always  knows  what's  news. 
(Reads  on  with  audible  fragments) 
"  Most  sensational  discovery  in  the  his- 
tory of  science  " — "  Greatest  achieve- 
ment of  the  human  intellect  " — "  Upsets 
Galileo,  Newton,  and  Euclid  "— "  Revo- 


vi  EASY  LESSONS  IN  EINSTEIN 

lution  in  philosophy  and  theology/ *  It 
looks  as  though  I  ought  to  know  some- 
thing about  this,  doesn't  it? 

The  Author:  I  think  you  will  have  to  sometime.  And 
you  might  as  well  do  it  now  and  get  it 
over  with. 

The  Reader  (running  down  the  column  and  hitting 
the  high  spots)  :  "  Parallel  lines  meet  " 
— "a  man  moving  with  the  speed  of 
light  never  grows  old  " — "  gravitation 
due  to  a  warp  in  space  " — "  length  of  a 
measuring  stick  depends  upon  direc- 
tion of  its  motion  " — "  mass  is  latent 
energy  " — "  time  as  a  fourth  dimen- 
sion " — why,  the  man  is  crazy,  isn't  he? 

The  Author:  Well,  definitions  of  insanity  are  so  un- 
certain that  it  is  not  safe  to  say  who  is 
crazy.  But  it  seems  there's  method  in 
his  madness — otherwise  how  could  he 
have  hit  upon  the  exact  extent  of  the 
sun's  attraction  on  light? 

The  Reader:  (Picks  up  his  paper  and  reads  aloud 
with  concentrated  attention)  "  Postu- 
late I.  Every  law  of  nature  which 
holds  good  with  respect  to  a  coordi- 
nate system  K  must  also  hold  good 


EASY  LESSONS  IN  EINSTEIN  vii 

for  any  other  system  K',  provided  that 
K  and  K'  are  in  uniform  movement  of 
translation."  Say,  do  you  know  any- 
thing about  this  business? 

The  Author:  Well,  yes,  a  little.  I  have  followed  the 
controversy — at  a  safe  distance — for  a 
number  of  years. 

The  Reader:  Can  you  tell  me  in  plain  language  what 
it  is  all  about? 

The  Author:  Yes.  Just  that.  I  .can  tell  you  what  it 
is  about,  though  I  can't  tell  you  what  it 
is.  Einstein  says  that  there  are  only 
twelve  men  in  the  world  capable  of 
understanding  his  latest  paper. 

The  Reader:  Are  you  one  of  the  twelve? 

The  Author:  No,  nor  the  thirteenth.  But  without 
plunging  into  the  mathematics  of  it,  we 
might  talk  over  some  of  the  interesting 
aspects  of  the  theory  of  relativity  and 
in  the  end  I  could  put  you  on  track  of 
the  twelve  so  you  could  read  up  on  the 
subject  if  you  liked. 

The  Reader:  All  right.  That's  fair.  This  is  a  slow 
car  anyhow.  Go  ahead. 

The  Author:  (See  following  pages) — 


EASY  LESSONS  IN  EINSTEIN 

"A  warp  in  nature  has  been  found, 
No  line  is  straight,  no  circle  round; 
For  Isaac  Newton  had  unsound 
Ideas  of  gravitation!' 

Why  is  it  that  our  newspapers  are  sending  out  their 
reporters  to  interview  astronomers  as  well  as  actresses 
and  devoting  pages  to  speculations  on  the  nature  of 
space  and  time  as  well  as  on  the  state  of  the  market? 
It  is — to  get  at  the  bottom  of  it — merely  because  a  few 
photographs  taken  during  the  eclipse  of  the  sun  on 
May  29,  1919,  by  two  telescopes,  one  at  Sobral  in 
northern  Brazil  and  the  other  on  the  island  of  Principe 
off  the  west  coast  of  Africa,  showed  an  abnormal  shift 
of  less  than  one-324,oooth  of  a  right  angle  in  the  posi- 
tion of  the  stars.  When  these  photograph  films  were 
laid  over  films  taken  before  the  eclipse  it  was  found 
that  the  star-images  about  the  darkened  disk  of  the 
sun  did  not  exactly  coincide  with  the  images  when  the 
sun  was  not  in  their  midst.  Measured  with  a  microm- 
eter the  displacement  of  the  stars  from  their  ordinary 
positions  was  found  to  be  i. 60  seconds  of  arc  on  the 

1 


2  EASY  LESSONS  IN  EINSTEIN 

African  plates  and  1.98  seconds  on  the  Brazilian  plates. 
Average  these  two  observations  and  you  get  1.79. 
This  is  extremely  close  to  the  1.73  predicted  by  Pro- 
fessor Einstein  of  Berlin  and  twice  as  large  as  the 
deflection  calculated  according  to  Newton's  law  of 
gravitation  which  would  be  .87  of  a  second. 

When  the  announcement  of  this  result  was  made  at 
the  meeting  of  the  Royal  Society  of  London  on  No- 
vember 6  all  eyes  were  turned  toward  Sir  Oliver 
Lodge,  for  last  February  he  had  been  rash  enough  to 
express  the  hope,  if  not  the  prediction,  that  the  results 
of  the  eclipse  expedition  would  support  Newton  rather 
than  Einstein.  But  instead  of  taking  part  in  the  dis- 
cussion Sir  Oliver  got  up  and  walked  out.  It  was 
suspected  that  he  had  "  gone  off  mad/'  as  we  Ameri- 
cans would  put  it,  because  the  starlight  would  not  fol- 
low his  preferred  path.  But  he  put  a  stop  to  any  such 
rumors  by  a  letter  to  The  Times  in  which  he  explains 
that  his  departure  was  not  due  to  any  dissatisfaction 
with  the  universe  but  to  the  necessity  of  catching  the 
6  o'clock  train.  He  frankly  acknowledges  that  "  the 
eclipse  result  is  a  great  victory  for  Einstein ;  the  quan- 
titative agreement  is  too  close  to  allow  much  room  for 
doubt "  but  he  adds  "  a  caution  against  a  strengthen- 
ing of  great  and  complicated  generalizations  concern- 
ing space  and  time  on  the  strength  of  this  splendid 


A  NEW  VIEW  OF  GRAVITATION  3 

result :  I  trust  that  it  may  be  accounted  for,  with  reas- 
onable simplicity  in  terms  of  the  ether  of  space." 

This  caution  is  wise,  but  we  cannot  hold  our  breath 
till  1922,  when  the  next  eclipse  comes,  to  see  if  these 
observations  are  verified  and  we  may  in  the  meantime 
consider  some  of  the  implications  of  Einstein's  theory 
of  relativity. 

Sir  Joseph  Thomson,  President  of  the  Royal 
Society,  in  making  the  momentous  announcement  in 
the  session  of  the  Society,  said : 

If  his  theory  is  right,  it  makes  us  take  an  entirely  new 
view  of  gravitation.  If  it  is  sustained  that  Einstein's 
reasoning  holds  good — and  it  has  sustained  two  very  se- 
vere tests  in  connection  with  the  perihelion  of  Mercury 
and  the  present  eclipse — then  it  is  the  result  of  one  of 
the  highest  achievements  of  human  thought.  The  weak 
point  in  the  theory  is  the  great  difficulty  in  expressing  it. 
It  would  seem  that  no  one  can  understand  the  new  law  of 
gravitation  without  a  thorough  knowledge  of  the  theory 
of  invariants  and  of  the  calculus  of  variations. 

What  is  this  theory  of  relativity  and  why  is  it  so 
important?  The  mathematics  of  it  are  too  much  for 
most  of  us,  but  we  can  get  some  notion  of  it  by  a 
familiar  illustration. 

Suppose  you  wake  up  some  morning  in  a  Pullman 
berth  and  look  fmt  of  the  window  to  see  where  you  are. 


4  EASY  LESSONS  IN  EINSTEIN 

You  find  your  view  blocked  by  a  passing  train  on  the 
next  track.  Now  if  you  do  not  feel  any  jar  of  your  car 
and  cannot  catch  sight  of  the  landscape  beyond  the 
other  train  you  cannot  tell  whether  (i)  your  train  is 
moving  forward  and  the  other  train  is  standing  still,  or 
(2)  your  train  is  standing  still  and  the  other  train  is 
moving  backward,  or  (3)  whether  both  trains  are 
moving  in  opposite  directions,  or  (4)  whether  both 
trains  are  moving  in  the  same  direction,  but  your  train 
faster.  It  is  obvious  that  the  trains  are  getting  past 
one  another.  You  can  measure  their  speed  of  parting 
as  accurately  as  you  please.  But  all  you  can  perceive 
is  the  relative  motion  of  the  two  trains.  You  begin 
to  wonder  whether  there  is  any  such  thing  as  abso- 
lute motion;  whether  there  is  any  real  difference  be- 
tween rest  and  motion.  Is  there  any  possible  way 
of  telling  whether  your  train  is  in  motion  or  not  if  all 
you  can  see  out  of  the  window  is  some  object  that 
itself  be  moving?  Suppose  the  windows  were  all  cur- 
tained, how  could  you  find  out  whether  you  were  mov- 
ing forward  or  backward  or  standing  still  ? 

You  discuss  this  curious  question  with  your  fellow 
passengers  at  the  breakfast  table  and  one  of  them 
makes  the  brilliant  suggestion  that  it  might  be  pos- 
sible to  determine  the  absolute  motion  of  the  car  by 
reference  to  the  air.  If  the  car  is  moving  forward  the 


RELATIVE  MOTION  ON  A  TRAIN          5 

air  would  stream  from  front  to  rear  and  the  reverse 
if  it  were  moving  backward.  "  Suppose,"  says  the  in- 
genious experimentalist,  "  that  you  stand  at  one  end 
of  the  car  and  I  at  the  other.  We  will  shout  at  each 
other  alternately  and  time  the  passage  of  the  sound 
with  our  stop  watches.  Since  sound  is  carried  by  air 
waves  it  will  take  longer  for  the  shout  to  go  against 
the  air  current  than  with  it,  and  from  that  measure- 
ment it  might  be  possible  for  us  not  only  to  determine 
which  way  the  car  is  moving  but  how  to  calculate  how 
fast  it  travels,  assuming,  of  course,  that  there  is  no 
wind  blowing."  That  strikes  you  as  a  crucial  experi- 
ment, but  you  point  out  one  possible  difficulty,  that  the 
doors  at  the  ends  of  the  car  may  be  closed  and  the 
air  inside  is  being  carried  along  with  the  car,  so  no 
difference  would  be  observable  in  the  speed  of  the 
sound  even  though  the  car  were  moving.  "  All  right," 
replies  your  scientific  friend,  "  we  will  make  a  pre- 
liminary test  to  see  if  the  enclosed  air  is  carried  along 
with  the  car,  and  if  we  find  that  it  is  not  then  we  will 
try  the  second  experiment  with  the  sound  signals  to 
see  which  way  the  air  current  is  moving.  These  two 
experiments  must  settle  it,  for  either  the  air  is  moving 
with  the  car  or  it  is  moving  through  the  car.  Can 
you  conceive  of  any  other  possibility  than  these  two?  " 
No,  you  cannot,  so  you  proceed  to  try  the  two  experi- 


6  EASY  LESSONS  IN  EINSTEIN 

ments.  First  you  visit  both  ends  of  the  car  and  find 
both  doors  open ;  the  air  then  is  not  being  carried  along 
with  the  car.  You  turn  then  with  confidence  to  the 
second  experiment  and  you  find,  of  course,  that  there 
is  a  difference  in  the  speed  of  sound  whether  it  moves 
with  the  air  drift  or  against  it. 

There  might,  I  admit,  be  practical  difficulties  in  the 
way  of  carrying  out  such  a  delicate  experiment  on  a 
moving  train,  but  we  need  not  bother  with  them,  for 
probably  the  current  of  air  through  the  car  would  be 
so  strong  as  to  blow  your  hat  out  of  the  back  door 
and  that  would  settle  the  question  to  your  satisfaction 
— or  at  least  it  would  settle  the  question  in  the  affirma- 
tive. 

But  imagine  your  amazement  if  this  second  experi- 
ment should  give  negative  results  like  the  first  one;  if 
you  could  detect  no  difference  in  time  whether  the 
sound  was  sent  forward  or  back  or  across  the  car. 
You  would  then  have  proved  by  experiment  (i)  that 
the  air  did  not  move  with  the  car  and  (2)  that  the  air 
did  not  move  through  the  car.  You  might  suppose 
from  this  that  your  car  is  at  rest,  but  suppose  the 
people  on  the  other  train  passing  yours  tried  the  same 
experiments  and  got  the  same  result,  namely,  that  they, 
too,  were  at  rest  as  regards  the  air.  You  would  then 
be  in  a  quandary,  for  your  two  indisputable  experi- 


CONTRADICTORY  EXPERIMENTS          7 

ments  had  apparently  given  contradictory  results.  You 
might  get  out  of  it  by  saying  that  there  was  no  air, 
but  if  not  what  carried  the  sound  waves — and  the 
hat? 

CONTRADICTORY  EXPERIMENTS 

Now  this  is  the  quandary  in  which  physicists  have 
been  in  for  the  last  thirty-three  years.  Is  there  any 
way  of  discovering  absolute  motion  among  the  heav- 
enly bodies  ?  We  can  observe  and  measure  with  great 
accuracy  their  relative  motion.  The  sun  is  seen  to 
pass  across  the  sky  from  east  to  west  and  man  at  first 
assumed  that  the  earth  was  still  and  the  sun  went 
around  it.  This  is  the  natural  and  instinctive  assump- 
tion, for  when  you  first  glance  out  of  your  Pullman 
window  you  get  the  impression  that  the  other  train 
is  the  moving  one.  But  for  the  last  three  hundred 
years  it  has  been  the  fashion  to  assume  the  earth  was 
moving  and  not  the  sun.  That  assumption  has  the 
advantage  of  simplifying  the  calculations  of  the  as- 
tronomers, though  I  never  could  see  why  we  should 
have  to  give  up  our  simple  notions  of  sunrise  and  sun- 
set to  save  them  a  little  trouble  figuring. 

The  earth  moves — if  it  does  move — so  quietly  and 
silently  that  we  feel  no  jar  or  engine-beat  to  tell  us  of 


8  EASY  LESSONS  IN  EINSTEIN 

its  motion.  If  the  earth  were  perpetually  shrouded 
by  clouds  could  we  find  out  its  motion  through  space 
or  even  its  rotation?  And  do  we  actually  get  any 
proof  on  this  point  from  observation  of  the  heavenly 
bodies  ?  We  see  them  moving  about  relatively  to  each 
other  and  we  can  represent  their  movements  most 
easily  by  supposing  that  the  moon  goes  around  the 
earth  and  that  the  earth  and  the  rest  of  the  planeta 
go  around  the  sun.  But  is  this  whole  solar  system  in 
motion?  So  it  seems  when  we  compare  it  with  the 
stars.  But  who  knows  if  the  solar  system  and  all  the 
visible  stars  are  not  altogether  moving  off  through 
space  at  the  rate  of  a  mile  or  a  thousand  miles  a 
second?  How  can  we  tell  unless  we  have  something 
that  is  still  and  fixed  to  measure  the  motion  by? 

It  seemed  until  recently  that  we  had  such  a  fixture, 
the  ether.  We  know  of  the  sun  and  stars  only  from 
the  light  that  comes  from  them  to  us.  Light,  as  we 
can  prove  by  simple  experiments,  consists  of  wave 
motion.  Now,  can  you  have  wave  motion  without 
something  to  wave?  Sound  waves  are  conveyed  by 
air  but  there  is  no  air  between  the  earth  and  the  sun. 
So  as  nothing  could  be  found  to  fill  this  empty  space 
scientists  had  to  invent  something  to  satisfy  their  sense 
of  the  fitness  of  things.  The  ether  was  the  product  of 
their  excogitations.  It  was  a  British  invention, 


THE  GALA  OF  THE  ETHER  9 

vised  in  the  Royal  Institution,  whence  have  come  so 
many  useful  theories  and  discoveries. 

The  ether,  as  Salisbury  said,  is  simply  the  nomina- 
tive of  the  verb  "  to  undulate."  It  was  conceived  of  as 
a  sort  of  transparent  jelly  filling  all  space,  more  rigid 
than  any  solid,  more  frictionless  than  any  fluid,  more 
easily  penetrateci  than  any  gas.  It  must  be  more  elastic 
than  steel  and  yet  so  rarefied  that  ordinary  matter 
passes  through  it  without  the  slightest  effort  The 
ether  is  supposed  to  slip  between  the  particles  of  the 
rushing  earth  as  the  wind  blows  through  the  branches 
of  a  tree. 

For  many  years  after  its  invention  the  ether  had 
•nothing  to  do  except  to  carry  light  about  from  one 
place  to  another.  But  when  the  electro-magnetic 
waves  of  the  wireless  telegraph  were  produced  some- 
thing was  needed  also  to  carry  them  and  this  new  task 
was  laid  upon  the  shoulders  of  the  uncomplaining 
ether.  When  Rontgen  discovered  the  X-rays,  whose 
waves  are  10,000  times  shorter  than  the  shortest  light 
waves,  these  were  turned  over  to  the  ether  to  run.  In 
fact,  it  got  so  that  whenever  a  physicist  found  any 
action  that  he  could  not  explain  by  ordinary  matter 
he  said :  "  Let  the  ether  do  it,"  and  that  hypothetical 
substance  apparently  answered  every  purpose  until  it 
came  to  this  question  of  relative  motion. 


10  EASY  LESSONS  IN  EINSTEIN 

Now  whatever  we  may  think  about  the  ether  it 
would  seem  that  if  there  is  any  such  thing  filling  all 
"  empty "  space  we  might  use  it  for  measuring  the 
motion  of  the  earth  through  it  as  we  did  the  air  cur- 
rent in  the  car.  If  the  earth  is  really  revolving  around 
the  sun  the  ether  must  be  whizzing  through  its  pores 
at  the  rate  of  about  nineteen  miles  a  second. 

But  wait — there  is  the  possibility  that  the  earth  car- 
ries along  with  it  in  its  flight  through  space  a  sort  of 
atmosphere  of  ether  as  it  does  of  air.  We  must  first 
get  rid  of  this  possibility  by  a  preliminary  experiment 
to  see  if  a  swiftly  moving  mass  of  matter  does  catch 
up  and  carry  along  with  it  a  little  of  the  ether.  This 
would  cause  a  sort  of  an  eddy  or  disturbance  in  the 
ether  in  the  neighborhood  of  the  moving  mass  as  a  boat 
disturbs  the  water.  For  instance,  a  ray  of  light  pass- 
ing close  to  a  rapidly  revolving  wheel  would  be  a 
little  deflected  and  show  a  distorted  image.  Sir  Oliver 
Lodge  tried  this  experiment  and  got  negative  results. 
That  is,  moving  matter  does  not  disturb  or  carry  with 
it  the  ether.  Consequently,  it  would  seem,  we  are 
left  to  the  only  other  logical  alternative,  that  the 
ether  drifts  through  matter  and  we  should  expect  to 
detect  this  drift  by  measuring  the  speed  of  light  in 
the  direction  of  the  earth's  motion.  It  ought  to  take 
longer  for  light  to  travel  from  one  point  to  another 


NEGATIVE  RESULTS  11 

if  the  earth  meantime  is  moving  away  from  the  first 
point  and  it  ought  to  take  less  time  if  the  earth  is 
moving  toward  it.  Well,  Michelson  and  Morley  tried 
this  experiment — and  also  got  negative  results!  It 
did  not  make  any  difference  whether  the  ray  of  light 
was  sent  in  the  direction  of  the  earth's  movement  or 
the  reverse  or  across  the  line,  it  traveled  invariably  at 
the  same  speed,  186,000  miles  a  second.  Here  then 
were  two  unquestionable  experiments  apparently  con- 
tradicting each  other.  One  proved  that  the  ether  did 
not  travel  with  the  earth.  The  other  proved  that  the 
ether  did  not  stand  still  while  the  earth  traveled 
through  it. 

Now  when  we  get  contradictory  answers  to  the  ques- 
tions we  put  to  Nature  "we  must  assume — unless 
Nature  is  nonsensical — that  we  are  asking  nonsensical 
questions.  If  in  the  trial  of  a  pickpocket  one  witness 
swears  that  the  thief  did  not  run  up  the  street  and 
another  witness  that  he  did  not  run  down  the  street 
the  lawyer  does  not  necessarily  say  that  one  of  them 
must  be  a  liar.  He  meditates  a  moment  and  then  it 
occurs  to  him  that  possibly  the  pickpocket  did  not  move 
or  that  perhaps  he  disappeared  into  the  third  dimension 
by  climbing  up  a  fire-escape  or  dropping  into  a  coal- 
hole. 

So  with  our  ether  quandary.    If  the  ether  does  not 


12  EASY  LESSONS  IN  EINSTEIN 

move  and  does  not  stand  still  perhaps  there  isn't  any 
ether  or  perhaps  there  is  a  fourth  dimension.  These 
are  two  conceivable  ways  out  of  the  dilemma  though 
they  are  not  easy  to  accept,  either  of  them.  If  there 
is  no  ether  what  carries  the  light  waves?  If  there  is 
a  fourth  dimension  in  what  direction  does  it  lie  ?  But 
it  is  no  harder  to  believe  in  or  conceive  of  a  fourth 
dimension  than  it  is  the  ether,  and  if  the  physicist  finds 
that  he  needs  it  in  his  business  he  will  have  to  have  it. 
Einstein  says  that  he  needs  a  fourth  dimension  for  his 
formulas. 


THE   CONUNDRUM  OF  THE  AGES 

For  twenty-four  hundred  years  philosophic  thought 
has  been  concerned  with  the  problem  of  the  relation 
of  space  and  time.  Drop  into  any  of  the  scientific 
societies  of  today  and  you  will  find  them  discussing 
whether  space  is  finite  or  infinite,  whether  there  is  any 
difference  between  rest  and  motion,  whether  length 
is  absolute  or  relative,  whether  time  and  space  have 
real  existence,  which  are  the  very  questions  discussed 
by  Pythagoras  and  Zeno  in  the  Greek  cities  of  Asia 
Minor.  Now  the  time  spent  in  these  speculations  has 
not  been  wasted,  although  it  has  led  to  no  definite 
conclusion,  for  out  of  it  have  grown  our  mathematics 


THE  CONUNDRUM  OF  THE  AGES        13 

and  physics.  The  Wandering  Jew,  who  is  the  only 
mortal  having  the  privilege  of  attending  the  schools  of 
the  Eleatics  and  those  of  the  present  day,  would  ob- 
serve one  difference,  that  modern  scientists  try  to  put 
their  theories  to  the  test  of,  experiment  wherever  pos- 
sible, while  the  ancients  were  content  with  thinking 
them  out. 

Of  all  the  guesses  that  have  been  given  to  this  rid- 
dle of  the  universe  none  has  been  more  bold  and  revo- 
lutionary than  that  contained  in  a  paper  of  four  or 
five  pages  contributed  in  1905  to  the  'Annalen  der 
Physik  by  Albert  Einstein.  The  controversy  it  precipi- 
tated has  not  altogether  been  confined  to  the  realm 
of  pure  reason,  for  scientists  are  but  human  and  as  such 
are  not  entirely  uninfluenced  by  patriotic  prejudice. 

In  this  brief  paper  he  proposed  a  new  theory  of  the 
universe  based  upon  two  postulates.  The  first  was 
the  principle  of  relativity;  that  3.ll»motion  is  relative. 
This  means,  for  instance,  that  we  would  never  know 
the  motion  of  a  smoothly  moving  train  if  the  windows 
were  darkened  and  that  we  could  never  discover  the 
forward  movement  of  the  earth  if  we  could  not  see  the 
heavenly  bodies. 

Einstein's  second  postulate  was  that  the  velocity  of 
light  is  independent  of  the  motion  of  the  source.  This 
is  a  hard  one  for  our  reason  to  swallow,  for  it  means 


14  EASY  LESSONS  IN  EINSTEIN 

that  nothing  can  travel  faster  than  light,  186,000  miles 
a  second,  and  that  you  cannot  make  light  travel  faster 
than  that  by  giving  it  a  swift  send-off.  It  is  the  same 
as  saying  that  if  a  man  standing  on  the  cowcatcher  of 
an  engine  threw  a  ball  forward,  it  would  not  make  any 
difference  with  the  velocity  of  the  ball  whether  the  train 
was  running  at  full  speed  forward  or  backward  or 
standing  still.  But  the  experiments  of  the  American 
physicists,  Michelson  and  Morley,  who  measured  the 
speed  of  light  and  found  it  the  same  whether  the  earth 
was  moving  toward  the  source  of  the  ray  or  away  from 
it,  or  at  right  angles  to  its  direction,  confirm  Einstein's 
second  assumption. 

If  we  accept  Einstein's  two  primary  postulates  and 
his  later  "  Principle  of  Equivalence  "  his  theory  clears 
up  this  ether-drift  difficulty  as  well  as  various  other 
riddles  of  the  universe.  It  explains  the  shifting  of  the 
orbit  of  Mercury  that  Newton's  theory  could  never 
account  for.  It  foretold  the  deflection  of  light  by  the 
sun's  gravitation  that  the  observations  on  the  eclipse 
of  last  May  confirmed.  A  third  test,  the  shifting  of 
the  lines  of  the  solar  spectrum  toward  the  red  end  in 
a  gravitational  field,  has  not  been  met.  Such  tech- 
nical points  concern  only  physicists  and  astronomers, 
but  Einstein's  relativity  theory,  which  two  out  of 
the  three  experiments  support,  carries  with  it  certain 


PARADOXES  OF  RELATIVITY  15 

speculations  as  to  time  and  space  that  are  upsetting  to 
current  conceptions. 

PARADOXES   OF   RELATIVITY 

All  three  of  Newton's  laws  of  motion  are  now 
questioned  and  the  world  is  called  upon  to  unlearn 
the  lesson  which  Euclid  taught  it  that  parallel  lines 
never  meet.  According  to  Einstein  they  may  meet. 
According  to  Newton  the  action  of  gravitation  is 
instantaneous  throughout  all  space.  According  to 
Einstein  no  action  can  exceed  the  velocity  of  light. 
If  the  theory  of  relativity  is  right  there  can  be  no  such 
thing  as  absolute  time  or  way  of  finding  whether  clocks 
in  different  places  are  synchronous.  Our  yardsticks 
may  vary  according  to  how  we  hold  them  and  the 
weight  of  a  body  may  depend  upon  its  velocity.  The 
shortest;  distance  between  two  points  may  not  be  a 
straight  line.  These  are  a  few  of  the  startling  im- 
plications of  Einstein's  theory  of  relativity.  If  he  had 
put  it  forward  as  a  mere  metaphysical  fancy,  as  a  pos- 
sible but  unverifiable  hypothesis,  it  would  have  aroused 
mere  idle  curiosity.  But  he  deduced  from  it  mathe- 
matical laws  governing  physical  phenomena  which 
could  be  put  to  the  test  of  experiment.  They  have  been 
tested  in  these  two  crucial  cases  and  prove  to  be  true. 


16  EASY  LESSONS  IN  EINSTEIN 

In  the  preceding  pages  we  have  discussed  the  ques- 
tion of  the  relativity  of  motion  and  seen  how  impossible 
it  is  to  tell,  for  instance,  whether  a  train  or  a  ship  you 
are  on  is  moving  or  not  unless  you  can  compare  it  with 
something  that  you  are  "  sure  "  is  stationary.  But 
what  are  you  sure  is  stationary?  Nothing  on  earth 
surely,  for  the  earth  compared  with  the  "  fixed  "  stars 
is  spinning  around  at  the  rate  of  about  a  thousand  miles 
an  hour  and  rushing  around  the  sun  at  the  rate  of 
nearly  70,000  miles  an  hour.  But  are  we  sure  the 
stars  are  fixed  since  we  have  nothing  else  to  compare 
them  with?  You  may  remember  Herbert  Spencer's 
illustration  of  the  sea  captain  who  was  walking  west  on 
the  deck  of  a  ship  sailing  east  at  the  same  rate.  Is  he 
moving  or  not?  If  you  are  in  the  same  boat,  you  say 
he  is.  If  you  are  on  shore  when  the  ship  is  passing 
you  say  he  is  standing  still  and  "  marking  time."  It 
all  depends  on  the  point  of  view. 

Now  you  may  readily  admit  that  all  motion  is  rela- 
tive, not  absolute,  and  yet  you  may  balk  at  the  idea 
that  space  and  time  are  also  relative,  not  absolute. 
But  motion  is  merely  simultaneous  change  of  position 
in  space  and  time,  and  why  should  we  feel  so  certain 
about  space  and  time  when  we  have  never  seen  either  ? 

You  may  say,  for  instance,  that  you  are  sure  your 
desk  is  so  long.  But  if  I  ask  you  how  long  you  have 


ARE  YOU  SURE  OF  YOUR  SHAPE?   17 

to  say  as  long  as  something  else.  You  may  say  it  is  a 
yard  long.  But  how  long  is  a  yard  ?  It  is  as  long  as 
some  tape  or  stick  marked  "  one  yard,"  and  this  in 
turn  has  been  taken  from  some  other  yardstick,  until 
you  get  back  to  the  brass  rod  in  London  that  is  just 
as  long  as  the  distance  from  the  tip  of  the  nose  of 
King  Henry  I  to  the  end  of  his  royal  thumb.  But  such 
a  standard  of  absolute  measurement  is  unsatisfactory 
to  everyone  except  an  absolute  monarchist.  But  apart 
from  the  difficulty  of  the  present  inaccessibility  of 
King  Henry's  nose  and  thumb,  can  we  be  confident  that 
our  yardstick  keeps  the  same  length  while  we  are 
measuring  with  it?  We  must  admit  indeed  that  it  is 
longer  on  a  summer  day  than  on  a  winter  day,  but  can 
we  be  sure  that  it  does  not  alter  in  length  when  we  hold 
it  upright  or  lay  it  horizontally  ?  Or,  rather,  could  we 
tell  if  it  did  change  in  length  as  it  is  changed  in  direc- 
tion? 

ARE  YOU  SURE  OF  YOUR  SHAPE? 

If  you  have  ever  been  in  any  of  those  funny  places  at 
the  amusement  parks  you  will  have  noticed  the  convex 
mirrors  there  and  how  ridiculous  they  make  other 
people  look.  If  you  cannot  afford  the  nickel  neces- 
sary for  the  study  of  optics  in  such  an  establishment 
you  can  contemplate  your  reflection  in  the  side  of  a 


18     EASY  LESSONS  IN  EINSTEIN 

shiny  tin  cup  or  can.  In  a  plane  mirror  you  see  a  man 
who  looks  as  you  suppose  yourself  to  be  except  that 
somehow  you  seem  to  have  become  left-handed.  But 
when  you  look  into  a  convex  cylindrical  mirror  set  up- 
right you  see  a  man  thinner  than  you  "  really  are." 
Look  into  the  same  mirror  set  horizontal  and  you  see 
a  man  shorter  than  you  "  really  are."  You  grin  at 
the  sight  of  such  queer-looking  creatures,  but  you 
notice  that  they  are  equally  amused  at  your  shape. 
Now  how  are  you  going  to  prove  to  the  men  in  the 
curved  glasses  that  they  are  mere  caricatures  and  that 
you  are  not  really  built  on  the  plan  of  either  of  these 
images?  You  naturally  resort  to  measurement,  as  a 
scientist  should.  You  cannot  get  into  the  mirror  world 
to  measure  the  tall  man  who  pretends  to  represent  you, 
but  you  can  explain  to  him  in  the  sign  language  what 
you  want  him  to  do  and  he  instantly  complies.  You 
stand  up  a  measuring  rod  at  your  side  and  show  him 
that  you  are  exactly  72  inches  tall.  He  also  sets  up  a 
rod  and  that  also  reads  72  inches.  Never  mind,  let  him 
use  any  kind  of  measure  he  likes,  you  will  catch  him 
when  it  comes  to  measurement  of  width  with  the  same 
stick.  You  hold  your  rule  across  your  shoulders  and 
it  reads  18  inches,  that  is,  one- fourth  your  height. 
But  he  also  measures  his  width  with  his  rule  and  makes 
it  just  the  same,  18  inches,  although  as  you  see  him  he 


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20  EASY  LESSONS  IN  EINSTEIN 

looks  at  least  six  times  as  high  as  he  is  broad.  Now 
you  are  sure  he  is  cheating — must  have  some  sort  of 
telescoping  rod  that  contracts  and  expands  according 
to  the  way  he  holds  it.  You  point  out  to  him  that  his 
measure  is  unreliable,  but  to  your  surprise  his  gestures 
seem  intended  to  convince  you  that  you  instead  are 
using  the  elastic  rule.  You  shake  your  fist  in  his  face — 
to  which  he  responds  with  equal  indignation — and  then 
you  turn  to  the  squatty  chap  in  the  other  mirror,  hop- 
ing he  will  be  amenable  to  reason.  But  he  also 
measures  himself  as  72  inches  high  and  18  inches  wide 
by  his  own  rule.  If  you  try  the  still  queerer-looking 
fellow  in  the  concavo-convex  mirror  who  is  distorted 
in  all  sorts  of  ways  you  will  find  that  his  rule  lengthens 
and  shortens  and  bends  just  enough  to  make  him  as 
symmetrical  a  man  as  yourself.  And  how  can  he  be 
otherwise  since  he  is  the  image  of  yourself? 

You  are  therefore  driven  to  doubt  the  in  variableness 
of  your  own  yardsticks.  Suppose  when  you  wake  up 
tomorrow  everything,  including  all  means  of  measur- 
ing, is  twice  as  big  as  it  is  today.  Could  you  tell  the 
difference?  Would  it  make  any  difference?  Would 
there  be  any  difference?  Is  there  any  such  thing  as 
absolute  distance  ?  Are  not  all  measurements  relative  ? 

Such  questions  had  from  the  earliest  times  occu- 
pied the  attention  of  speculative  philosophers,  but  they 


THE  MICHELSON-MORLEY  EXPERIMENT    21 

passed  from  the  realm  of  metaphysics  to  the  realm 
of  physics  in  1886  when  Michelson  and  Morley  made 
their  famous  experiment  on  the  speed  of  light  in  vari- 
ous directions.  Their  object  was  to  find  out  if  the 
ether,  the  hypothetical  medium  carrying  the  light 
waves,  was  stationary  and  drifted  back  through  the 
earth  as  the  earth  moved  onward.  They  devised  an 
instrument  of  such  delicacy  that  the  stamp  of  a  foot 
a  hundred  yards  off  would  be  noticeable.  A  ray  of 
light  was  divided  into  two  parts;  one  half  was  sent 
forward  and  back  in  the  direction  toward  which  that 
part  of  the  earth  where  the  experiment  was  made 
was  moving  at  the  time;  the  other  half  was  sent  back 
and  forth  across  the  line  of  this  motion.  But  the  two 
rays  of  light  following  different  routes  came  back  at 
the  same  instant  and  matched  up  exactly.  In  order  to 
correct  for  any  inequality  in  the  instrument,  Michelson 
and  Morley  turned  it  around  so  the  arm  that  formerly 
pointed  across  the  line  of  motion  now  pointed  in  the 
direction  of  that  motion  and  the  other  arm  pointed 
across,  but  that  made  no  difference.  The  light  traveled 
with  the  same  velocity  regardless  of  the  motion  of  the 
earth. 

This  negative  result  was  just  as  astonishing  as  if 
you  should  stand  at  a  certain  spot  on  the  bank  of  a 
river  half  a  mile  wide  and  should  send  out  two  boats, 


22  EASY  LESSONS  IN  EINSTEIN 

one  to  go  up  the  river  half  a  mile  against  the  current 
and  then  back  with  the  current  and  the  other  boat  to 
go  across  the  river  and  back.  If  both  boats  should 
return  at  the  same  moment  you  would  be  puzzled  to 
account  for  it.  One  way  of  accounting  for  it  would 
be  that  your  measurement  of  the  half-mile  course  up- 
stream had  been  a  little  short.  This  was  the  explana- 
tion of  the  Michelson-Morley  experiment  given  by  the 
Dutch  physicist,  Lorentz.  He  suggested  that  the  arm 
of  the  instrument  shortened  a  trifle  as  it  was  turned 
from  across  the  line  of  the  earth's  motion  to  the  direc- 
tion of  that  motion.  The  amount  of  shrinkage  neces- 
sary to  compensate  for  the  ether  drift  would  be  exceed- 
ingly small.  Besides  how  could  you  measure  the 
change  in  the  length  of  the  arm  if  the  rule  you  laid 
alongside  of  it  altered  in  the  same  proportion? 
Lorentz's  explanation  could  not  be  disproved,  yet  it 
was  so  upsetting  to  our  ordinary  ideas  of  the  stability 
of  matter  that  it  was  hard  to  accept. 

Einstein  took  Lorentz's  idea  and  made  it  one  of  the 
fundamental  principles  of  his  new  theory  of  the  uni- 
verse and  then  deduced  from  this  theory  sundry  very 
startling  conclusions,  some  of  which  could  be — and 
have  been — confirmed  by  experiment.  According  to 
Einstein  the  size  and  shape  of  any  body  depends  upon 
the  rate  and  direction  of  its  movement.  For  ordinary 


MOTION  CHANGES  DIMENSIONS         23 

speeds  the  alteration  is  very  slight,  but  it  becomes 
considerable  at  rates  approaching  the  speed  of  light, 
186,000  miles  a  second.  If,  for  instance,  you  could 
shoot  an  arrow  from  a  bow  with  a  velocity  of  160,000 
miles  a  second,  it  would  shrink  to  about  half  its  length, 
as  measured  by  a  man  remaining  still  on  earth.  A 
man  traveling  along  with  the  arrow  could  discover  no 
change.  No  force  could  bring  the  arrow  or  even  the 
smallest  particle  of  matter  to  a  motion  greater  than  the 
speed  of  light,  and  the  nearer  it  comes  to  this  limit  the 
greater  the  force  required  to  move  it  faster.  This 
means  that  the  mass  of  a  body,  instead  of  being  abso- 
lute and  unalterable  as  we  have  supposed,  increases 
with  the  speed  of  its  movement.  Newton's  laws  of 
dynamics  are  therefore  valid  only  for  matter  in  mo- 
tion at  such  moderate  speeds  as  we  have  to  deal  with 
in  our  experiments  on  earth  and  in  our  observations  of 
the  heavenly  bodies.  When  we  come  to  consider 
velocities  approximating  that  of  light  the  ordinary 
laws  of  physics  are  subject  to  an  increasing  cor- 
rection. 

If  a  person  calculates  that  he  is  attaining  a  speed 
faster  than  light  he  will  seem  to  another  observer 
to  be  moving  the  other  way.  That  is,  any  motion 
above  the  speed  of  light  is  negative  motion.  Just  as 
a  tourist  traveling  more  than  12,000  miles  away  from 


24  EASY  LESSONS  IN  EINSTEIN 

home  in  any  direction  will  really  be  getting  nearer 
home  the  farther  he  goes. 

Such  speculations  would  not  have  bothered  any- 
body twenty  years  ago,  for  then  the  physicist  did  not 
have  to  handle  any  cases  of  such  high  speeds.  But 
when  radium  was  discovered  it  was  found  that  this 
metal  was  continuously  throwing  off  particles  of  nega- 
tive electricity  with  approximately  the  speed  of  light. 
Now  if  these  electrons  are  not  matter  they  are  at  any 
rate  the  material  of  which  matter  is  made.  They  can 
be  detected  and  counted  and  tracked  and  deflected  and 
speeded  and  weighed.  They  are  very  real  things,  per- 
haps the  ultimate  reality  of  all  things,  yet  their  ex- 
treme velocity  carries  them  out  of  Newton's  world 
and  into  Einstein's. 

INTRODUCING  THE  FOURTH   DIMENSION 

Now  Einstein's  world,  as  I  said  before,  differs  from 
the  world  in  which  we  are  accustomed  to  live  in  many 
particulars.  It  has  four  dimensions  instead  of  three. 
One  of  these  dimensions  may  be  time.  Time,  too,  must 
be  relative,  not  absolute.  This  is  even  harder  to 
imagine  than  the  relativity  of  space. 

As  some  schoolboy  said :  "  If  there  were  no  matter 
in  the  universe  the  law  of  gravitation  would  fall  to 


L 


WHAT  IS  MEANT  BY  DIMENSIONS 

No  dimensions: 

A   mathematical   point. 

Has  position   but  no  size. 

Represented  by  a  dot.  Like  this 

One  dimension: 

Has  length  but  no  breadth. 

Made  by  moving  a  point  along  straight  in  any  direction. 

Represented  by  a  line.  Like  this 

Tvro  dimensions: 

A  plane  surface  like  this  page. 

Has  length  and  breadth  but  no  thickness. 

Made  by  moving  a  line  in  a  direction  perpendicular  to  its 
length  (that  is,  into  the  second  dimension. 

Represented  by  two  straight  lines  of  indefinite  length  per- 
pendicular to  each  other. 

The  lines  are  called  axes  and  are  labeled  x  and  y. 

The  point  where  they  meet,  the  origin,  is  marked  O. 

Like  this 

Three  dimensions: 

A  solid  like  a  cube. 

Has  length,  breadth  and  thickness. 

Made  by  moving  a  plane  in  a  direction  perpendicular  to  the 
other  two  (that  is,  into  the  third  dimension). 

Cannot  be  pictured  on  paper,  but  is  indicated  by  three  axes, 
xt  y,  and  s,  of  which  x  and  y  are  on  the  plane  of  the 
page  and  *  is  supposed  to  be  stuck  up  at  right-angles  to 
the  other  two.  Stick  a  pin  into  the  paper  at  the  point 
O  and  you  will  have  the  third  or  z  axis.  Like  this 

Four  dimensions:  i 

Has  length,  breadth,  thickness  and  extension  into  a  fourth 

dimension,  say  time  . 
Made  by  moving  a  cube  in  a  direction  perpendicular  to  the 

other  three  (that  is,  into  the  ofurth  dimension). 
Cannot  be  pictured  on  paper,  but  may  be  indicated  by  four 

axes,  x,   y,  z  and  t   (or  «),   each  at  right-angles  to  the 

other  three.  Like  this 

More  dimensions: 

Any  desired  number  of  dimensions  can  be  worked  out  " 
mathematically  but  with  increasing  difficulty  because  of 
the  impracticability  of  diagrammatical  representation.  We 
can  generalize  the  idea  by  speaking  of  a  "  geometry  of  n 
dimensions"  where  «  may  stand  for  any  number  what- 
ever from  zero  to  infinity. 

A  line  of  a  given  length  contains  an  infinite  number  of  points, 
A  square  of  a  given  size  contains  an  infinite  number  of  lines. 
A  cube  of  a  given  size  contains  an  infinite  number  of  plane  squares. 
A  tesseract  (four-dimensional  cuboid)  of  a  given  size  contains  an  infinite 
number  of  solid  cubes. 


26     EASY  LESSONS  IN  EINSTEIN 

the  ground."  Quite  so.  And  what  would  there  be 
left  of  space  if  you  took  everything  out  of  it,  and  what 
would  become  of  time  if  nothing  ever  happened?  In 
other  words  are  not  space  and  time  merely  forms  of 
thought,  the  framework  of  ideas,  and  if  so  cannot  we 
fix  them  over  to  suit  our  need  of  new  conceptions? 
As  a  matter  of  fact  we  do.  We  have  constructed  by 
the  aid  of  Euclid  and  his  successors  a  geometry  of 
three  dimensions  that  works  perfectly  for  all  ordinary 
requirements  and  if  we  need  a  fourth  dimension  to 
accommodate  these  new  astronomical  and  physical 
phenomena  we  will  build  on  the  necessary  addition  to 
our  conception  of  space.  There  was  no  use  having  a 
fourth  dimension  so  long  as  we  had  nothing  to  put 
in  it.  For  ordinary  earth  measurements  (geo-metry) 
such  as  laying  out  a  town  lot  we  only  use  two  dimen- 
sions, length  and  breadth.  We  speak  of  "  flat  ground  " 
and  "  water-level "  regardless  of  the  fact  that  all  our 
"  straight "  lines  on  the  earth's  surface  are  really 
curves  that  come  back  to  us  after  going  25,000  miles 
or  less.  It  is  only  when  measuring  mile  lengths  that 
we  have  to  correct  for  the  curvature  of  the  earth  in 
the  third  dimension.  So  if,  as  seems  probable,  we  shall 
have  to  make  allowance  in  astronomical  measurements 
for  the  curvature  of  the  universe  in  a  fourth  dimension 
it  will  merely  mean  a  little  labor  to  the  astronomers  and 


INTRODUCING  THE  FOURTH  DIMENSION    27 

it  will  relieve  their  minds  of  some  of  their  perplexities. 
There  is  nothing  more  mystical  or  mysterious  or 
"  psychical "  about  a  fourth  dimension  than  about  the 
other  three.  A  dimension  is  simply  a  measurable  direc- 
tion and  we  can  use  five  dimensions  or  n  dimensions  if 
we  need  to. 

It  does  not  matter  that  we  cannot  "  see  "  a  figure 
in  four  dimensions  even  with  our  mind's  eye.  Actually 
we  cannot  see  any  figure  of  more  or  less  than  two 
dimensions:  we  have  to  take  the  others  on  faith. 
Nobody  can  see  the  mathematician's  point  because  it 
has  no  dimensions,  no  size  at  all.  The  schoolboy  says : 
"  Let  that  be  the  point  A,"  and  we  let  it  be  although 
what  he  is  pointing  at  with  his  stick  is  not  a  point  but 
a  vast  irregular  splotch  of  white  chalk  on  the  black- 
board. So,  too,  we  cannot  see  a  mathematical  line  be- 
cause it  has  only  one  dimension,  length  and  no  breadth. 
But  set  four  lines  at  right  angles  to  one  another  and  we 
get  a  square.  This  we  can  really  see  if  the  enclosed 
surface  is  of  a  different  color  such  as  a  shadow  or 
black  print.  Set  six  squares  together  at  right  angles 
and  we  get  a  cube.  This  we  cannot  see  in  its  entirety 
at  one  time.  All  that  we  see  when  we  look  squarely 
at  a  cube  is  a  square.  If  we  look  at  it  from  an  angle 
we  see  what  looks  like  a  square  with  a  couple  of 
lozenges  on  the  sides.  The  retina  of  the  eye  is  prac- 


HOW  TO  DRAW  A  FOUR-DIMENSIONAL  FIGURE 


The  best  way  to  get  an  idea  of  the  construction  of  a  cubical 
solid  in  four  dimensions  is  to  draw  a  diagram  yourself  and  trace 
out  in  turn  each  of  the  eight  cubes  that  inclose  it.  I  am  indebted 
to  K.  W.  Lamson  of  Barnard  College  for  the  following  sketch 
and  directions: 

Draw  the  four  coordinate  axes  OX,  OY,  OZ,  OU. 

Lay  off  the  unit  chat  on  the  X  axis,  a\a,i  on  the  Y  axis,  a\ai 
on  the  Z  axis  and  aibi  on  the  U  axis. 

Draw  the  cube  OtOnasCkCkaeaia*  on  the  three  axes  XYZ. 

Draw  parallel  to  this  the  cube  bibibabtb&bebib*  on  the  U  axis. 

Draw  the  cube  aiOaaaaibibzbab*  on  the  three  axes  XYU.  This  is 
partly  drawn  already. 

Draw  parallel  to  this  the  cube  aiOtcisCkbibabsbt  on  the  three  axes 
XYU. 

This  completes  the  figure. 

There  are  four  other  cubes  in  the  figure  besides  thos« 
described  above: 


The  cube  on  the  XZU  axes  Oiatbibtaiatbiba  and  its  opposite 
&sdtiMte&BOfc 

The  cube  on  the  YZU  axes  ckOzfhaibsbibibi  and  its  opposite 
btbtbtbi. 

The  figure  has:  16  corners,  32  edges,  24  bounding  squares, 
8  bounding  cubes. 

The  heavy  line  aib*  might  be  called  the  principal  diagonal  and 
makes  an  angle  of  60  degrees  with  each  of  the  four  axes.  It  is 
foreshortened  in  the  sketch,  but  its  real  length  is  twice  that  of 
one  edge  of  the  cube.  Every  line  except  this  is  on  the  outside 
of  the  four-dimensional  figure. 


THE  TESSERACT 

A  four-dimensional  cube-like  solid  if  transparent  and  looked 
at  with  one  eye  would  appear  something  like  this.  But  it  is 
obviously  impossible  to  depict  a  four-dimensional  figure  on  a 
two-dimensional  surface  like  this  page. — From  "  The  Fourth 
Dimension  Simply  Explained,"  Munn  and  Company,  N.  Y. 


30  EASY  LESSONS  IN  EINSTEIN 

tically  a  plane  surface,  so  all  we  can  get  is  a  two- 
dimensional  projection  of  a  solid.  Since  our  two  eyes 
present  us  slightly  different  pictures  of  an  object  we 
infer  from  these  its  size,  shape  and  distance,  but  this  is 
guesswork. 

Still  we  have  a  pretty  clear  idea  of  a  cube  although 
we  have  never  seen  it  in  its  solidity.  But  the  attempt 
to  visualize  the  hypercube,  the  four-dimensional  figure 
corresponding  to  the  cube,  strairis  our  imagination  to 
the  breaking  point.  Some  mathematicians  endowed 
with  constructive  imaginations  of  high  power  claim  to 
have  got  by  long  hard  thinking  some  sort  of  a  shadowy 
and  fleeting  perception  of  it,  but  their  visions — if  they 
are  not  imaginary — do  not  help  out  us  ordinary  folks. 
But  if  we  cannot  imagine — that  is,  image — the  hyper- 
cube  we  know  all  about  it,  even  its  name.  It  is  called 
the  "  tesseract,"  and  it  is  bounded  by  eight  cubes  just 
as  the  cube  is  bounded  by  six  squares  and  the  square 
by  four  lines.  The  tesseract  has  24  square  faces,  32 
edges  and  16  rightangular  corners. 


TIME  AS   THE   FOURTH   DIMENSION 

Although  we  find  it  hard  to  conceive  of  a  fourth 
dimension  in  space  we  have  no  such  difficulty  in  case 
the  fourth  dimension  is  time.  In  fact,  we  use  this  idea 


TIME  AS  THE  FOURTH  DIMENSION     31 

all  the  while  and  could  not  get  along  without  it.  To  fix 
the  position  of  any  event  requires  four  dimensions. 
For  instance,  a  man  is  shot.  Where?  At  the  corner 
of  7th  Avenue  and  42d  Street,  New  York.  This  fixes 
the  place  by  two  coordinates  crossing  at  right  angles 
in  a  plane.  But  was  it  above  or  below  this,  on  the 
twentieth  floor  of  the  Times  Building  or  in  the  Sub- 
way ?  Knowing  this  fixes  the  third  dimension,  but  we 
have  still  to  fix  its  position  in  a  fourth  dimension,  time. 
Was  it  today  or  last  week  and  what  hour?  If  then  we 
find  out  all  four  we  can  distinguish  this  shooting  from 
any  that  may  have  occurred  in  other  places  at  the 
same  time  or  at  other  times  in  the  same  place. 

Or  consider  this  simple  illustration :  Cut  a  strip  of 
motion  picture  film  into  its  separate  scenes  and  pile 
them  up  in  order  till  it  is  as  high  as  it  is  broad.  You 
have  then  a  cubical  event.  Two  dimensions  of  the  cube 
are  spatial;  the  third  dimension  is  essentially  temporal, 
although  in  a  spatial  form.  If  one  of  the  films  from 
the  middle  of  the  pack  represents  the  present  then  the 
films  below  represent  the  past  and  those  above  the 
future.  The  people  on  the  picture  you  picked  out  know 
only  of  the  scene  there  depicted  though  they  may  have 
a  fading  memory  of  the  past  and  a  dim  anticipation  of 
the  future.  But  to  you  who  are  outside  of  the  film  pack 
all  the  scenes  are  equally  visible.  They  are  all  present 


32  EASY  LESSONS  IN  EINSTEIN 

to  you.  This  is  the  way  most  Christians  have  con- 
ceived of  God,  as  one  to  whom  past  and  future  form 
one  eternal  present,  so  he  sees  simultaneously  all  things 
that  have  been,  are  or  will  be. 

If  our  pile  of  film  were  made  up  of  snapshots  taken 
one  a  day  throughout  a  man's  life  we  should  see  at 
one  glance  his  growth  from  babyhood  to  boyhood,  to 
maturity  and  old  age.  We  could  turn  the  leaves  of  his 
life  backward  or  forward  as  we  will.  Some  day  per- 
haps we  shall  have  stereo-movies,  scenes  in  three 
dimensions  with  time  as  the  fourth. 

This  idea  of  time  as  a  fourth  dimension  is  not  a 
new  one.  In  1754  d'Alembert,  defining  "  dimension  " 
in  the  Encyclopedia,  wrote :  "  A  brilliant  man  of  my 
acquaintance  believes  that  one  may  regard  duration  as 
a  fourth  dimension."  In  1903  Minkowski  worked  out 
the  idea  in  mathematical  form.  H.  G.  Wells,  always 
quick  to  catch  up  a  new  scientific  theory  to  use  as  a 
plot  for  a  story,  wrote  in  1895  of  "  The  Time 
Machine,"  a  vehicle  by  which  a  man  could  travel  back 
and  forth  in  time  as  he  can  travel  east  and  west  in  a 
motor  car.  In  this  he  visits  the  future  and  finds  man- 
kind split  into  two  species,  a  subterranean  working 
class  living  on — literally — a  pleasure-loving  leisure 
class. 

In  "  The  Plattner  Case  "  Wells  tells  of  a  chemical 


TIME  AS  THE  FOURTH  DIMENSION     33 


professor  who  was  by  an  explosion  knocked  into — not 
the  middle  of  next  week  as  we  commonly  say — but 


A          B  a1         a  s-         a- 

In  space  of  three  dimensions  we  cannot  make  a  right  hand 
glove  and  a  left  hand  glove  look  the  same  no  matter  how  we 
turn  them  around.  But  if  we  turn  one  glove  inside  out  it  will 
match  the  other  except  that  the  lining  now  appears  on  the 
outside. 


Our  two  hands  cannot  be  turned  inside  out  so  as  to  look  the 
same  in  three  dimensions,  though  they  might  in  four  dimensions. 

into  the  fourth  dimension  of  space.    Ten  days  later 
he  was  knocked  back  again  into  our  world  but  the  only 


34  EASY  LESSONS  IN  EINSTEIN 

evidence  of  the  truth  of  his  story  was  that  his  heart 
beat  on  the  right  side  and  he  was  left  handed  and  other- 
wise reversed  in  a  way  that  would  be  impossible  in 
a  space  of  three  dimensions.  We  can  turn  a  glove 
inside  out  in  three  dimensions  and  so  make  it  just  like 
its  mate  of  the  other  hand,  but  we  cannot  turn  a  solid 
inside  out  except  in  four-dimensional  space. 

In  another  of  his  "  Thirty  Strange  Stories  "  Wells 
tells  "  The  Story  of  Davidson's  Eyes."  While  David- 
son wasN  working  in  his  London  laboratory  a  lightning 
shock  so  affected  his  eyesight  that  he  could  not  see 
the  familiar  objects  about  him  which  he  could  feel  but 
looked  instead  at  a  South  Sea  island  on  the  opposite 
side  of  the  globe.  This  might  be  possible  in  a  curved 
space  of  four  dimensions  although  Wells  professes 
to  pooh-pooh  such  an  absurd  suggestion  while  he  in- 
geniously insinuates  it.  George  Macdonald  in  his 
fantastic  romance  "  Lilith  "  also  introduces  the  fourth 
dimension. 

Points  that  are  far  apart  if  measured  in  three  di- 
mensions may  be  close  together  in  the  fourth.  We  can 
readily  understand  this  if  time  is  the  fourth  dimension, 
for  events  can  happen  at  the  same  instant  thougfh 
thousands  of  miles  apart.  But  it  is  not  impossible  to 
conceive  of  the  fourth  dimension  as  spatial  instead  of 
temporal  if  we  approach  the  problem  from  a  simpler 


LIFE  IN  FLATLAND  35 

standpoint.  Let  us  think  of  ourselves  as  living  in  a 
"  Flatland  "  of  two  dimensions  with  no  thought  of  a 
third.  There  yet  survive  in  enlightened  America  in- 
dividuals who  believe  that  "  the  sun  do  move  "  and  who 
deny  that  the  earth  is  "  round  like  a  ball."  That  is, 


8' 

/?' 

B' 

-H 

R' 

R 

B 

* 

B'      B'  /?' 


a  B 

By  movement  in  one  dimension  we  cannot  make  the  lines  AB 
and  B'A'  coincide  for  if  we  drag  B'A'  straight  on  to  AB  the 
ends  will  not  match.  But  if  we  swing  B'A'  around  through  the 
second  dimension  we  bring  it  on  AB  so  the  letters  correspond. 

they  do  not  recognize  the  curvature  of  the  earth  in  the 
third  dimension.  But  if  such  an  individual  were  to 
travel  in  a  "  straight  "  line  westward  over  the  "  level  " 
land  and  water  he  would,  much  to  his  surprise,  come 
back  to  his  starting  point  which  he  had  left  25,000 
miles  behind  him. 


36  EASY  LESSONS  IN  EINSTEIN 


B 

A 

a       c 


C'         IF 


In  space  of  two  dimensions,  such  as  a  table  top,  we  cannot 
bring  these  two  triangles  into  the  same  position.  If  we  drag 
one  straight  over  on  to  the  other  (movement  in  one  dimension) 
they  will  not  fit  together.  If  we  swing  one  triangle  around 
(movement  in  two  dimensions)  they  still  do  not  fit.  But  if 
we  take  one  triangle  off  the  table  and  turn  it  over  (movement 
in  the  third  dimension)  we  can  then  lay  it  by  the  side  of  the 
other  and  they  will  match  perfectly. 


A  WORM'S-EYE  VIEW  OF  THE  WORLD     37 


A   WORM  S-EYE  VIEW   OF   THE  WORLD 

Suppose  yourself  a  worm — the  Bible  says  you  are 
anyway — and  crawling  around  on  a  sheet  of  paper. 
With  your  vermicular  mind  you  doubtless  would  take 
a  superficial  view  of  the  universe  and  find  it  as  im- 
possible to  imagine  a  third  dimension  as  man  does  a 


fourth.  If  in  the  course  of  your  crawling  you  came 
across  a  triangle  you  might — if  you  were  a  measuring 
worm — pace  it  off  and  find  that  the  distance  from  A 
to  B  was  8  inches,  from  B  to  C  was  6  inches  and  from 
this  data,  if  you  knew  the  law  of  the  hypothenuse,  you 
might  calculate  that  the  distance  from  A  to  C  was  10 
inches.  On  measuring  it  you  would  find  your  predic- 
tion verified  and  so  gain  perfect  confidence  in  your 
plane  geometry.  But  unbeknownst  to  you,  poor  worm 
with  your  eyes  fixed  on  the  paper,  some  man  may 
have  picked  up  the  sheet  and  crumpled  it  up  or  rolled  it 
over  so  that  A  and  C  are  only  one  inch  apart — in  the 


38  EASY  LESSONS  IN  EINSTEIN 

third  dimension.  The  worm  is  right  when  he  thinks 
the  distance  between  these  points  is  10  inches :  so  is  the 
man  right  when  he  says  it  is  one  inch.  It  depends  on 
the  point  of  view. 

Now  in  Einstein's  view  something  of  this  sort  hap- 
pens to  our  three-dimensional  space  when  matter  gets 
into  it.  We  know  for  instance  that  if  you  divide  the 
circumference  of  any  circle  by  the  diameter  the  ratio 
figures  out  as  3.1415+.  It  has  been  calculated  to  707 
decimal  places  but  we  can  dispense  with  the  rest  of 
them  and  call  the  whole  thing  Pi  for  short.  Write 
it  in  Greek  as  it  and  it  looks  more  learned.  Now  if 
you  place  a  heavy  particle,  say  a  lead  bullet,  in  the 
center  of  a  circle  the  ratio  of  the  diameter  to  the  cir- 
cumference, according  to  Einstein,  becomes  a  little 
less  than  Pi,  for  the  circle  has  been  warped,  so  to 
speak,  into  the  fourth  dimension  by  the  strain  of 
gravitation.  The  difference  in  such  a  case  is  too  small 
to  be  measurable  by  any  known  means,  but  it  is  sup- 
posed to  be  an  actual,  not  an  imaginary,  deviation  from 
the  geometrical  law. 

Now  the  sun  being  a  big  heavy  body  must  extend  its 
gravitational  strain  for  a  considerable  distance  around 
and  a  ray  of  light  passing  through  this  crumpled  up 
space  would  not  be  able  to  pursue  a  straight  course. 
And,  according  to  the  eclipse  observations,  it  does  not. 


THE  EASIEST  WAY  IS  SHORTEST       39 

Light  like  everything  else  follows  "  the  easiest  way  " 
and  this  is  not  always  the  straight  and  narrow  path. 
A  river  takes  the  easiest,  not  the  shortest,  way  to  the 
sea  and  this  leads  it  through  many  meanderings.  Most 
of  us,  I  suppose,  have  a  mental  image  of  Newton's 
gravitation  as  a  sort  of  rope  by  which  the  sun  pulls  the 
earth  into  its  orbit  when  it  is  disposed  to  fly  off  on  a 
tangent  But  from  Einstein's  viewpoint  we  should 
rather  think  of  the  earth  as  picking  its  way  as  best  it 
can  through  a  space-and-time  combination  that  has 
been  strained  and  distorted  by  the  power  of  the  sun. 
I  visualize  Einstein's  solar  system  as  a  spider  web  with 
the  sun  in  the  middle  like  the  spider  and  the  planets 
like  flies  trying  to  get  around  through  the  tangled 
strands.  But  it  is  more  complicated  than  that  for 
each  planet  has  its  own  lesser  web  of  radiating  in- 
fluence to  drag  about  with  it  wherever  it  goes. 

Newton's  idea  is  simpler,  but  unfortunately  light 
at  least  seems  to  follow  Einstein's  law,  not  Newton's. 
That  is  why  Einstein  is  such  a  troublesome  fellow.  If 
he  would  confine  himself  to  metaphysical  speculation 
nobody  need  bother  about  these  strange  notions  of  his. 
But  when  he  points  how  they  can  be  proved  and  then 
British  astronomers  and  American  physicists  find 
things  according  to  his  deductions  he  cannot  be  ig- 
nored. The  man  does  not  seem  to  have  that  decent  re- 


40  EASY  LESSONS  IN  EINSTEIN 

•spect  for  the  opinions  of  mankind  that  leads  most  of 
us  to  limit  our  logic  to  the  sphere  of  common  sense. 
When  he  gets  an  idea  in  his  head  he  follows  it  wher- 
ever it  leads  him  even  though  he  bumps  up  against 
Euclid  and  Newton  and  the  rest  of  us.  For  instance, 
if  you  admit  the  second  of  his  two  fundamental  postu- 
lates, that  the  speed  of  light  is  constant,  regardless  of 
the  velocity  of  its  source,  you  are  irresistibly  led — 
unless  you  let  go  of  his  hand  somewhere  on  the  way — 
to  the  conclusion  that  time  is  a  local  affair;  that  there 
is  no  way  of  telling  by  light  signals  whether  two  clocks 
at  a  distance  are  keeping  the  same  time,  or  whether  two 
events  at  different  places  occur  simultaneously.  You 
could  not  tell  this  even  if  you  could  shoot  a  watch 
from  one  place  to  the  other  with  the  speed  of  light,  for 
not  matter  how  many  seconds — or  years — the  watch 
might  be  on  its  way  it  would  register  the  same  time. 
If  instead  of  a  watch  a  man  could  travel  at  that  speed 
he  would  not  grow  old  on  the  way.  According  to 
Einstein  no  man,  watch  or  any  other  material  thing 
can  travel  with  the  speed  of  light,  for  it  would  require 
an  infinite  force  to  give  the  smallest  particle  such  a 
velocity.  But  let  us  suppose  that  a  hollow  projectile 
holding  a  man,  such  as  Jules  Verne  and  Wells  used  on 
their  voyages  to  the  moon,  should  be  sent  off  into 
space  with  a  velocity  one  twenty-thousandth  less  than 


TURNING  TIME  BACKWARD  41 

light.  If  at  the  end  of  a  year  the  projectile  should 
be  caught  like  a  comet  by  the  gravitation  of  some  star 
and  be  swung  around  and  sent  back  to  the  earth,  the 
man  on  stepping  out  of  his  shell  would  be  two  years 
older  but  he  would  find  the  world  two  hundred  years 
older.  This  would  be,  as  Professor  Langevin  suggests 
in  Scientia,  1911,  an  interesting  way  to  study  history, 
but  it  would  be  risky,  not  to  say  impossible.  Still 
French  scientists,  like  Napoleon,  have  no  place  in  their 
dictionaries  for  so  stupid  a  word  as  "  impossible  "  and 
M.  Esnault-Pelterie  has  figured  out  that  a  thousand 
pounds  of  radium  would  be  sufficient  to  cary  a  man  to 
Venus  in  35  hours  if  a  hollow  projectile  could  be  fitted 
up  like  a  rocket  with  the  radium  in  the  rear  sending 
out  a  rapid  fire  of  electrons. 

TURNING  TIME   BACKWARD 

To  loosen  up  our  conventional  ideas  of  the  fixity  of 
time  and  space  we  may  accept  the  aid  of  the  scientific 
romancers.  Camille  Flammarion,  the  famous  French 
astronomer,  wrote  a  fantastic  little  book  called 
"  Lumen  "  which  tells  of  a  man  who  died  in  1864.  His 
soul  flew  straight  to  its  heaven  which  was  one  of  the 
planets  of  Capella,  the  largest  star  in  the  constellation 
Auriga.  Here  he  found  the  benevolent  inhabitants 


42     EASY  LESSONS  IN  EINSTEIN 

of  that  sphere,  who  were  endowed  with  superhuman 
powers  of  sight,  watching  with  great  distress  the 
bloody  scenes  of  the  French  revolution  of  1793,  and 
wondering  how  it  would  come  out.  To  the  visitor 
from  the  earth  this  was  an  old  story,  to  the  people 
of  Alpha  Aurigae  it  was  a  present  spectacle,  for  the 
distance  of  the  star  was  such  that  it  took  light  72  years 
to  travel  from  the  earth,  so  they  were  72  years  belated 
in  their  observation  of  current  events  on  our  planet. 
The  spirit  of  the  defunct  Parisian,  having  the  power 
of  flying  through  empty  space  at  any  speed  he  chose, 
found  that  he  had  thereby  also  acquired  control  of 
time  and  could  hasten,  retard,  stop  or  reverse  the 
course  of  events  at  will  by  simply  varying  his  speed. 
If  he  remained  stationary,  scenes  on  the  earth  would 
unfold  at  their  normal  rate  and  in  regular  order.  If  he 
traveled  away  from  the  earth  with  the  speed  of  light 
everything  seemed  to  stand  still.  If  he  traveled  faster 
than  light  he  overtook  the  rays  that  had  left  the 
earth  farther  and  farther  back  in  the  past  so  he  saw 
through  them  events  in  the  reverse  order.  For  instance 
when  he  looked  down  on  Waterloo  he  saw  the  battle- 
field strewn  with  corpses  and  Napoleon  walking  toward 
Waterloo  backward  pushing  his  horse  by  the  bridle. 
This  is  how  the  battle  looked  to  the  interspatial  ob- 
server : 


TURNING  TIME  BACKWARD  43 

When  my  sight  was  sufficiently  habituated  to  the  scene, 
I  perceived  some  soldiers  coming  to  life  out  of  the  eternal 
night,  and  by  a  single  effort  standing  up.  The  dead 
horses  revived  like  the  dead  cavaliers,  and  the  latter 
remounted  them.  As  soon  as  two  or  three  thousand  men 
had  returned  to  life,  I  saw  them  form  unconsciously  in 
line  of  battle.  The  two  armies  took  their  places  fronting 
one  another,  and  began  to  fight  desperately  with  a  fury 
that  one  might  have  taken  for  despair.  As  the  combat 
deepened  on  both  sides,  the  soldiers  came  to  life  more 
rapidly.  .  .  . 

At  each  gap  made  by  the  cannon  in  the  serried  ranks 
a  group  of  resuscitated  dead  filled  up  the  gaps  immedi- 
ately. When  the  belligerents  had  spent  the  whole  day 
in  tearing  one  another  to  pieces  with  grape-shot,  with 
cannons  and  bullets,  with  bayonets,  sabers  and  swords 
— when  the  great  battle  was  over,  there  was  not  a  single 
person  killed,  no  one  was  even  wounded ;  even  uniforms 
that  before  it  were  torn  and  in  disorder  were  in  good 
condition,  the  men  were  safe  and  sound,  and  the  ranks 
in  correct  form.  The  two  armies  slowly  withdrew  from 
one  another,  as  if  the  heat  of  the  battle  and  all  its  fury 
had  no  other  object  than  the  restoration  to  life,  amid 
the  smoke  of  the  combat,  of  the  two  hundred  thousand 
corpses  which  had  lain  on  the  field  a  few  hours  before. 
What  an  exemplary  and  desirable  battle  it  was ! 

Another  literary  curiosity  on  the  same  theme  is 
"  Ignis  "  by  Comte  Didier  de  Chousy.  This  tells  of 
certain  engineers  who  attempted  to  utilize  the  internal 
heat  of  the  earth  by  running  the  waters  of  a  lake  into 


44  EASY  LESSONS  IN  EINSTEIN 

a  deep  boring.  The  result  was  an  explosion  that  blew 
off  a  piece  of  the  planet.  But  the  passengers  on  this 
artificial  asteroid  on  looking  down  through  their  well 
at  the  earth  they  had  left  could  see  the  lake  and  city 
undisturbed  and  watch  themselves  at  work  as  they  were 
before  the  place  blew  up.  The  explanation  was  that 
this  fragment  of  the  earth  was  projected  into  space 
more  rapidly  than  the  speed  of  light  and  so  was  catch- 
ing up  with  the  rays  that  had  gone  out  before  the  ex- 
plosion; these  rays,  of  course,  carried  the  picture  of 
earlier  scenes.  But  Einstein  would  say  that  this  story 
— as  we  might  ourselves  have  suspected — must  be  fic- 
tion for  according  to  his  theory  the  speed  of  light  is  the 
absolute  limit  of  motion,  the  infinity  of  velocity,  which 
no  material  body  may  excel  or  attain.  He  does  not, 
however,  say  anything  about  the  possible  speed  of  a  dis- 
embodied spirit  such  as  Flammarion  employed  in  his 
imaginary  exploration  of  space. 


THE   METAPHYSICS   OF  THE   MOVIES 

But  from  such  fantasies  we  can  see  that  the  order  in 
which  we  view  events  depends  upon  how  fast  and  in 
what  direction  we  are  moving  and  that  past  and  future 
may  be  reversed  to  our  vision.  This  is  easily  made 
apparent  by  means  of  motion  pictures.  If  the  film  is 


THE  METAPHYSICS  OF  THE  MOVIES    45 

reeled  off  in  the  wrong  direction  the  action  is  reversed. 
So  we  see  divers  rising  gracefully  out  of  the  water  and 
landing  on  the  spring  board.  Newly  hatched  chickens, 
dismayed  at  the  sight  of  this  unfriendly  world,  calmly 
tuck  themselves  back  into  their  broken  shells  which 
close  in  upon  them.  When  we  have  come  to  the  close 
of  a  perfect  Thanksgiving  Day  the  obliging  operator 
may  give  us  an  encore  of  the  dinner  reversed  by  run- 
ning his  machine  backward.  Then  we  see  pieces  of 
turkey  politely  picked  out  of  the  mouths  of  the 
diners  with  their  forks  and  replaced  upon  the  plates. 
When  these  are  passed  back  to  the  carver  he  puts  the 
slices  neatly  in  their  places  and  the  fowl  is  then  sent 
back  to  the  oven  to  be  unroasted.  The  cook  then  sticks 
on  the  feathers.  The  hired  man  carries  the  turkey  out 
to  the  chopping  block  where  with  one  swift  stroke  he 
restores  the  head  and  the  fowl  runs  off  backwards. 
This  is  just  as  correct  as  the  ordinary  order.  The 
sequence  of  events  is  the  same.  Cause  and  effect  are 
linked  together  as  firmly  as  before,  only  they  have  ex- 
changed places.  A  scientist  knowing  nothing  of  our 
world  except  from  watching  such  reversed  motion 
pictures  might  deduce  from  them  the  same  consistent 
and  logical  system  of  natural  laws  that  we  now  have 
although  some  of  them,  for  instance,  the  second  law  of 
thermo-dynamics,  would  be  reversed  in  form. 


46  EASY  LESSONS  IN  EINSTEIN 

The  motion-picture  man  has  also  the  power  to  alter 
the  speed  of  the  passage  of  time  as  he  will  by  turning 
the  crank  faster  or  slower.  Sometimes  he  is  quite 
too  careless  in  the  way  he  employs  this  prerogative.  If 
he  is  behind  time  on  his  schedule  he  will  rush  through 
a  lazy  siesta  scene  in  a  Mexican  plaza  with  all  the  fury 
of  a  Mack  Sennett  farce.  But  this  telescoping  of  time 
can  be  used  to  advantage  as  when  he  shows  us  the 
growth  of  a  plant,  the  unfolding  of  its  flower  and  the 
ripening  of  its  fruit,  all  in  fifteen  minutes.  On  the 
other  hand  motion  may  be  slowed  up  by  taking  twice 
as  many  pictures  a  minute  as  usual  and  projecting  them 
at  the  ordinary  rate.  For  instance,  if  it  is  a  dog  jump- 
ing up  to  grab  a  piece  of  meat  from  his  master's  hand, 
we  see  the  dog  rise  slowly  from  the  ground  and,  while 
poised  in  mid-air,  eye  the  meat  carefully  to  select  the 
best  point  of  attack,  then  deliberately  take  it  between 
his  jaws  and  gradually  descend.  Now  notice  that  this 
is  just  as  true  a  picture  of  the  dog's  jump  as  any  other. 
The  movie  man  has  simply  expanded  time  measure- 
ments as  he  expands  space  measurements  when  he 
shows  us  a  close-up.  A  close-up  with  a  face  covering 
a  sixteen- foot  screen  is  just  as  true  as  a  smaller  picture. 
It  is  what  we  should  always  see  if  the  lens  of  our  eyes 
were  a  bit  more  convex.  We  look  through  the  small 
end  of  an  opera-glass  and  objects  seem  magnified.  We 


DURATION  IS  SUBJECTIVE  47 

look  through  the  large  end  and  objects  seem  minified. 
This  is  not  an  illusion.  The  opera-glass  does  actually 
enlarge  or  reduce  what  we  see. 

So,  too,  time  intervals  can  be  lengthened  or  short- 
ened. Take  a  dose  of  hashish — no,  don't — I  should 
say,  if  you  did  take  a  dose  you  would  find  that  your 
perception  of  duration  was  prolonged.  If  while  under 
the  influence  of  the  drug  you  drop  a  book  it  will  seem 
an  hour  getting  to  the  ground.  De  Quincey  describes 
such  experiences  in  his  "  Confessions  of  an  Opium 
Eater."  But  without  entering  into  such  abnormal 
states  we  all  know  by  everyday  experience  how  time 
flies  or  lags  according  to  the  number  of  our  sensations. 
Bergson's  philosophy  is  built  upon  the  distinction  be- 
tween the  idea  of  duration  as  experienced  by  all  of  us 
and  the  idea  of  time  as  established  by  the  physicists 
for  comparative  measurements. 

We  live  in  deeds  not  years ;  in  thoughts  not  breaths ; 
In  feelings  not  in  figures  on  a  dial. 

— Festus. 

i 

For  all  we  know  an  ephemeral  insect  that  dies  in  a  day 
may  live  a  longer  life  than  a  Galapagos  turtle  that 
exists  for  two  centuries. 

What  Mark  Twain  said  about  classical  music  applies 
also  to  science;  "  It  is  not  so  bad  as  it  sounds."    The 


48  EASY  LESSONS  IN  EINSTEIN 

thing  that  the  chemist  calls  "  sodium  chloride  "  other 
folks  call  "  salt " — and  so  does  he  when  he  is  off  duty. 
Don't  let  the  scientist  bluff  you  by  his  polysyllablic 
propensity.  Just  try  to  see  what  he  means  by  such 
language.  Now  what  these  new-fashioned  non- 
Euclidean  geometricians  call  "  the  four-dimensional 
space-time  continuum  "  is  essentially  the  same  system 
of  reference  as  you  have  used  ever  since  you  could 
toddle.  Minkowski  did  not  invent  it.  Everybody 
thinks  that  way  unless  he  is  an  idiot.  Each  one  of  us 
has  had  to  build  up  his  own  philosophy  of  the  universe 
long  before  we  went  to  school,  mostly  before  we  could 
talk.  We  had  to  study  geometry  while  we  were  in  our 
cradles — worse  than  that  we  had  to  work  out  a  practi- 
cal system  of  geometry  for  ourselves  without  the  help 
of  Euclid  or  anyone  else.  We  had  to  excogitate  a 
system  of  relationship  between  the  sights  and  sounds 
and  touches  that  came  to  us  before  we  could  get  along 
in  the  world.  Probably  we  all  solve  this  riddle  of  the 
universe  in  about  the  same  way  although  since  there  is 
no  way  of  directly  comparing  notes  we  cannot  be  sure 
about  that 

THE  EGOCENTRIC   THEORY  OF  THE  UNIVERSE 

But  the  framework  that  we  construct  to  hold  every- 
thing outside  of  ourselves  is  essentially  of  the  following 
form: 


EGOCENTRIC  THEORY  OF  THE  UNIVERSE    49 

You  are  the  center  of  your  universe.  Everything 
and  every  event  that  you  are  considering  is  related  to 
you  here  and  now.  Starting  from  this,  your  point  of 
place  and  time,  you  imagine  eight  straight  lines  stretch- 
ing out  toward  infinity  in  eight  directions  as  divergent 
as  possible.  These  lines — call  them  destinations  or  di- 
rections or  dimensions  or  coordinates  as  you  please — 
consist  of  four  opposing  pairs,  right  and  left,  up  and 
down,  forward  and  back,  future  and  past.  Somewhere 
along  or  between  these  four  dimensional  lines  that  cross 
in  your  brain  you  can  find  a  place  for  anything  that  you 
need;  your  pencil,  the  discovery  of  America,  the  sun 
and  next  Friday.  You  can  connect  up  all  these  things 
by  lines  which  may  represent  changes,  that  is  the  tracks 
of  movements  in  space  and  time.  To  connect  the  pencil 
in  your  hand  with  the  discovery  of  America  you  would 
have  to  count  back  428  years  on  the  time  line  and 
measure  off  on  the  east-west  and  north-south  lines 
whatever  distance  you  may  be  from  San  Salvador — 
not  to  consider  the  motion  of  the  earth. 

Anything  that  exists,  that  is  to  say,  persists,  is  mov- 
ing along  the  time  dimension  at  what  appears  to  be  a 
uniform  rate.  Of  course  you  can,  if  you  like,  conceive 
of  time  itself  as  a  stream  flowing  through  things. 
Since  all  motion  is  relative,  that  way  of  looking  at  it 
is  just  as  "  true  "  as  the  other.  But  it  is  simpler  and 


50  EASY  LESSONS  IN  EINSTEIN 

more  sensible  to  think  of  things  moving  through  a  sta- 
tionary time  just  as  we  think  of  them  moving  through 
a  stationary  space.  A  material  point  that  is  at  rest, 
such  as  the  dot  of  an  i  on  this  page,  (we  continue  to 
disregard  the  motion  of  the  earth)  is  not  moving  about 
in  space  but  is  moving  forward  in  time.  Its  track  then 
is  a  straight  line  along  the  time  dimension.  That  is, 
a  material  point  is  a  line  in  the  fourth  dimension.  If 
you  move  the  page  to  the  right  the  forward  movement 
of  the  dot  of  the  i  in  the  time  dimension  is  combined 
with  the  sideways  motion  in  a  single  slanting  line.  If 
you  move  the  page  simultaneously  upward,  rightward 
and  backward  the  track  of  the  point  is  a  line  combin- 
ing the  movement  in  all  four  dimensions.  Such  a 
track  of  a  point  moving  through  space  and  time  is 
called  its  "world-line."  It  is  a  continuity  of  one 
dimension.  Any  event  is  the  point  of  intersection 
of  one  or  more  such  world  lines  and  we  can  never 
observe  anything  except  such  intersections.  That 
is  to  say,  everything  happens  somewhere  and  some- 
time. 

A  picture  flashed  on  a  cinema  screen  has  three  di- 
mensions. It  is,  say,  10  feet  long  and  6  feet  high 
and  lasts  1-16  of  a  second,  but  it  has  no  thickness.  A 
man  necessarily  has  four  dimensions.  He  may 
measure  from  24  to  72  inches  in  one  dimension,  from 


BERGSON  ON  TIME  51 

8  to  1 8  inches  in  the  second,  from  4  to  9  inches  in  the 
third  and  70  years  in  the  fourth. 

After  all,  the  idea  of  the  relativity  of  time  ought  to 
be  easier  to  accept  than  that  of  space  for  it  is  in  accord 
with  experience  instead  of  contrary  to  it.  We  drop  off 
to  sleep  and  wake  the  next  instant  if  we  credit  our 
personal  perceptions.  Why  should  we  believe  the  sun 
and  the  clock  in  preference  to  ourselves? 

Bergson  bases  his  whole  philosophy  upon  the  dis- 
tinction between  duration  as  it  is  felt  by  the  individual 
while  he  is  living  through  it  and  time  as  it  is  employed 
by  the  physicist  in  his  calculations.  The  latter  con- 
ception, physical  time,  is,  as  Bergson  says,  a  mere  in- 
vention of  man  and  virtually  a  fourth  dimension  of 
space,  so  he  concludes: 

To  sum  up;  every  demand  for  explanation  in  regard 
to  freedom  comes  back,  without  our  suspecting  it,  to  the 
following  question :  "  Can  time  be  adequately  represented 
by  space  ?  "  To  which  we  answer :  Yes,  if  you  are  deal- 
ing with  time  flown ;  No,  if  you  speak  of  time  flowing.* 

Past  and  future  are  alike  to  the  physicist,  differing 
only  in  direction,  like  east  and  west.  But  to  the  living 
person  they  are  altogether  different  things.  For  man 
rolls  up  his  past,  as  a  tourist  his  rug,  and  carries  it  with 

>     *  Bergson:  "Time  and  Free  Will,"  p.  221. 


52  EASY  LESSONS  IN  EINSTEIN 

him  wherever  he  goes.  That  is  why  Wells's  "  Time 
Machine  "  and  the  reversed  reels  of  the  movies  are  so 
funny.  There  is  nothing  absurd  about  running  a  wheel 
backward  but  there  is  about  running  a  man  backward.* 
The  physicist  feels  no  reluctance  about  turning  the 
stream  of  time  backward  for  all  physical  phenomena 
are  reversible  under  the  proper  conditions.  If  we  in- 
terpret the  universe  as  merely  matter  in  motion  and 
imagine  at  a  certain  instant  that  every  individual  par- 
ticle reverses  its  motion  and  goes  in  just  the  opposite 
direction  at  the  same  speed,  then  the  whole  history  of 
the  world  would  be  reenacted  in  the  opposite  order  and 
the  earth  would  return  to  its  primeval  nebulae. 

In  Wells's  story,  "  The  New  Accelerator/'  a  profes- 
sor invents  an  elixir  that  speeds  up  the  rate  of  living  a 
thousandfold.  A  person  taking  a  dose  of  it  sees  people 
as  wax  figures  apparently  motionless  in  the  midst  of 
violent  action.  Falling  objects  seem  to  stand  still  in  the 
air.  The  music  of  a  band  is  reduced  to  "  a  low-pitched, 
wheezy  rattle  "  or  "  the  slow  muffled  ticking  of  some 
monstrous  clock."  But  in  compensation  for  this  the 
accelerated  drug-fiend  could  watch  at  leisure  the  slow 
flapping  of  a  bee's  wings. 

But  even  Wells  with  his  seven-league-boots  imagina- 


*Bergson  in  his  "Laughter"  traces  all  humor  back  to  this 
fundamental  absurdity  of  making  a  man  act  mechanically. 


THE  MAGNIFICATION  OF  MOTION       53 

tion  finds  it  difficult  to  keep  ahead  of  the  march  of 
science.  What  he  then  saw  only  with  his  mind's  eye  we 
can  actually  observe.  By  moving  the  accelerating  lever 
on  your  phonograph  toward  the  S  end  of  the  scale  you 
can  slow  up  the  tune  and  lower  its  pitch  until  it  becomes 
inaudible  as  music.  The  new  Pathe  ultra-rapid  camera 
can  take  pictures  at  the  rate  of  160  to  the  second. 
When  these  are  projected  on  the  screen  at  the  usual 
rate  of  16  to  the  second  all  movement  takes  place  ten 
times  slower  than  in  actual  life.  This  gives  oppor- 
tunity for  the  study  in  detail  of  the  action  of  a  ball- 
player pitching  a  curve  or  of  the  wing  motion  of  a 
humming  bird  or  of  the  splash  of  a  marble  falling  into 
water  or  of  the  flight  of  a  bullet.  We  can  magnify 
motion  or  minify  it  as  much  as  we  will.  The  cinemat- 
ograph owes  its  origin  the  desire  of  Senator  Leland 
Stanford  to  study  the  movement  of  a  horse's  legs  so 
as  to  find  out  why  one  racer  went  faster  than  another. 
Such  playful  flights  of  the  scientific  imagination  as 
Wells  and  Flammarion  indulge  in  and  such  freaks  of 
projection  as  the  camera  man  amuses  us  with  are  of 
use  to  those  of  us  who  find  difficulty  in  translating  a 
mathematical  formula  into  terms  of  everyday  life. 
There  is  no  better  place  to  study  metaphysics  than  in 
the  world  of  the  flickering  screen,  for  there  man  has 
complete  control  of  time  and  space.  He  can  enlarge 


54  EASY  LESSONS  IN  EINSTEIN 

and  reduce  any  object.  He  can  hasten,  retard  or 
reverse  any  action.  He  can  throw  upon  the  screen 
at  the  same  time  events  happening  months  and  miles 
apart.  Therefore  to  those  of  us  who  have  had  the 
advantage  of  an  education  in  the  movies,  Einstein's 
ideas  of  the  relativity  of  time  and  space  do  not  seem 
startling  or  inconceivable. 

Kant  not  only  conceived  the  possibility  of  more  than 
three  dimensions  but  believed  in  the  probability  of  it. 
His  argument  is  based  on  greater  insight  into  the  in- 
tentions of  the  Almighty  than  we  of  this  day  would 
claim : 

"  If  it  is  possible  that  there  be  developments  of  other 
dimensions  in  space,  it  is  also  very  probable  that  God  has 
somewhere  produced  them.  For  His  works  have  all  the 
grandeur  and  variety  that  can  possibly  be  conceived." 

In  this  temporal,  spatial  and  material  world  of  ours 
reality  requires  that  the  four  dimensions  should  hang 
together.  But  at  an  infinite  distance  from  all  matter 
this  fourfold  combination  would  be  dissolved  into  a 
three-dimensional  space  and  a  one-dimensional  time, 
In  that  extra-mundane  realm  time  ceases  to  flow,  gravi- 
tation no  longer  drags  downward,  matter  is  non-ex- 
istent, light  is  immovable  and  change  is  impossible.* 

*  "  We  can  thus  say  that  all  these  paradoxical  phenomena  (or 
rather  negations  of  phenomena)   which  have  been  enumerated 


LOOKING  AT  YOUR  BACKHAIR  55 

Thus  the  new  mathematics  leads  to  a  state  curiously 
like  the  conventional  conception  of  heaven. 

We  talk  as  our  forefathers  did  about  "  the  ends  of 
the  earth  "  but  we  know  that  one  might  start  from 
his  home  and  walk  forever  in  any  direction  without 
coming  to  an  end  of  it.  But  though  the  earth's  sur- 
face is  infinite  in  the  sense  of  endless,  yet  one  never 
can  get  more  than  8,000  miles  away  from  home  wher- 
e'er he  may  roam.  If  a  man  stood  on  the  top  of  the 
highest  mountain  on  earth  and  aimed  a  level  gun  in 
any  direction,  the  bullet,  if  it  could  be  given  sufficient 
velocity  to  counteract  the  influence  of  gravity,  would  go 
around  the  world  and  hit  him  in  the  back  of  the  head. 
Or  if  light  were  sufficiently  deflected  by  gravitation  to 
follow  a  level  line  around  the  earth — another  absurd 
assumption — the  man  looking  through  a  level  telescope 
in  any  direction  could  see  how  his  hair  was  combed  in 
the  back.  Such  happenings,  though  impossible,  are  not 
inconceivable  but  are  logical  consequences  of  our 
knowledge  that  the  world  is  round  and  that  what  we 
call  straight  or  level  lines  as  measured  on  plain  or  sea 
are  really  great  circles  around  a  center  four  thousand 
miles  below. 

Now  is  it  not  also  conceivable  that  the  lines  we  call 


above  can  only  happen  after  the  end  or  before  the  beginning 
of  eternity"  (De  Sitter). 


56  EASY  LESSONS  IN  EINSTEIN 

straight  in  astronomical  space  may  also  have  an  im- 
perceptible curvature  in  some  unknown  fourth  dimen- 
sion? If  this  curve  is  closed  like  the  circumferences 
of  the  earth  a  ray  of  light  pursuing  a  straight  course  in 
a  certain  direction  might  eventually  return  upon  its 
track,  even  though  not  refracted  or  reflected  by  the 
matter  it  passes  through  or  by.  A  telescope  of  un- 
limited power  pointed  into  space  at  a  tangent  might 
then  show  the  observer  his  own  back,  if  light  were 
transmitted  instantaneously,  but,  since  it  is  not  and 
since  the  curvature  of  space,  if  there  be  any,  is  ex- 
ceedingly minute,  what  the  observer  would  see,  assum- 
ing that  the  earth  had  come  back  to  its  former  position, 
might  be  the  scenes  of  some  geological  age  millions  of 
years  ago. 

NON-EUCLIDEAN   GEOMETRY 

The  idea  that  space  itself  may  be  curved  and  that  the 
axioms  and  assumptions  on  which  our  geometry  since 
the  time  of  Euclid  have  been  based,  may  not  be  abso- 
lutely and  exactly  and  eternally  and  universally  true 
has  been  diligently  studied  during  the  last  fifty  years. 
The  Russian  Lobatchewsky,  the  Hungarian  Bolyai  and 
the  German  Riemann  have  developed  systems  of  geom- 
etry by  starting  from  premises  the  opposite  of  those 
of  Euclid  and  these  systems  are  just  as  logical  and  con- 


NON-EUCLIDEAN  GEOMETRY  57 

sistent  with  themselves  as  the  ordinary  or  Euclidean 
geometry.  These  non-Euclidean  geometries  were  at 
first  commonly  regarded  as  mere  freaks  of  the  mathe- 
matical imagination,  but  they  have  already  proved  valu- 
able in  leading  to  a  reconsideration  of  the  fundamental 
principles  of  our  thinking  and,  if  Einstein  is  right,  they 
may  be  necessary  to  explain  physical  phenomena.  It 
is  hard  for  the  mathematician  to  discover  anything 
useless.  A  distinguished  American  mathematician  in 
announcing  a  new  theorem  exclaimed :  "  And  thank 
Heaven,  no  possible  use  can  ever  be  found  for  it."  But, 
whatever  it  was,  he  made  a  rash  boast  for  nowadays 
the  mechanic  treads  on  the  heels  of  the  mathematician 
and  uses  imaginary  quantities,  actual  only  in  the 
fourth  dimension,  like  V — i,  in  figuring  out  the  wind- 
ing of  his  dynamo. 

Readers  whose  mathematical  faculty  is  weak  or  un- 
developed and  who  like  something  concrete  with  "  hu- 
man interest "  in  it  will  find  what  they  want  in  "  Flat- 
land  by  A  Square,"  a  book  published  in  Boston  in  1891. 
The  author,  who  turned  out  to  be  the  Reverend  Edwin 
Abbott,  tells  of  a  land  in  only  two  dimensions.  The 
ruling  class  consisted  of  polygons,  the  bourgeoisie  of 
squares  and  equilateral  triangles,  the  lower  class  of 
isosceles  triangles  of  narrow  base,  while  the  criminals 
had  more  irregular  forms  and  the  women  were  mere 


58     EASY  LESSONS  IN  EINSTEIN 

needles.  Since  all  were  confined  to  a  surface,  four 
lines  set  in  a  square  made  a  tight  prison.  The  inhabi- 
tants of  Flatland,  even  the  aristocratic  and  intellectual 
individuals  who  had  so  many  sides  as  to  be  almost 
circular,  could  not  conceive  of  a  third  dimension  from 
which  a  person  like  ourselves  could  look  down  and  see 
at  a  glance  the  insides  of  their  houses,  their  safes  and 
their  bodies  just  as  a  being  in  the  fourth  dimension 
could  see  the  insides  of  ours.  The  narrator,  that  is,  A 
Square  of  Flatland,  visits  as  a  missionary  the  land  of 
two  dimensions  where  all  the  people  lie  in  a  line  and 
refuse  to  believe  in  anything  outside  it  and  finally  he 
encounters  and  endeavors  to  convert  a  solitary  point 
of  no  dimensions  but  finds  him,  as  we  should  expect, 
an  incorrigible  solipsist. 

We  should  all  of  us  have  been  familiar  with  the 
fourth  dimension  for  years  if  Slade  had  not  turned  out 
a  trickster.  Slade  was  an  American  medium — the  orig- 
inal of  Browning's  "  Mr.  Sludge  " — who  fooled  Pro- 
fessor Zollner  by  giving  him  what  purported  to  be  ex- 
perimental evidence  of  the  fourth  dimension.  Zollner 
was  a  distinguished  German  physicist,  Professor  of 
Astronomy  in  the  University  of  Leipzig,  old,  near- 
sighted, pre-disposed  to  spiritualism,  and  unskilled  in 
legerdemain.  Any  proofs  that  Zollner  asked  for,  Slade 
was  usually  able  at  the  next  seance  to  produce.  All  the 


NON-EUCLIDEAN  GEOMETRY 


59 


O  B* 


In  space  of  one  dimension   (a  straight  line)  there  could  be 
neither  bend,  loop  nor  knot  in  a  string. 


In  space  of  two  dimensions  (a  flat  surface)  a  double  bend 
could  be  made  in  the  string  but  no  loop  or  knot  could  be  made. 


B    B' 


But  if  we  raise  one  string  (into  the  third  dimension)  and  lay 
it  over  the  other  like  this : 


*  B      B' 

We  get  a  loop  but  cannot  form  a  knot  without  using  the  ends. 


A  knot  like  this  cannot  be  made  in  a  string  so  long  as  the 
ends  are  held  by  the  hands.  But  if  we  could  use  a  fourth  dimen- 
sion we  could  tie  such  a  knot  as  easily  as  we  made  a  bend  by  the 
use  of  the  second  dimension  and  a  loop  by  the  use  of  the  third. 
If  such  a  knot  could  be  tied  in  a  string  so  held  it  would  be 
experimental  evidence  of  the  existence  of  four-dimensional 
space. 


60  EASY  LESSONS  IN  EINSTEIN 

things  that  one  might  do  in  four  dimensions  but  could 
not  do  in  three  were  forthcoming  by  the  obliging  spirits 
whom  Slade  had  at  call.  Zollner  tied  the  ends  of  a 
string  together  and  sealed  them  on  the  table  top,  letting 
the  loop  hang  down  under  the  table  out  of  sight.  He 
then  asked  to  have  a  single  knot  tied  in  the  string  and 
the  spirits  tied  four.  Zollner  also  reports  that  the 
coins  he  put  into  a  sealed  box  were  taken  out  and  writ- 
ing produced  inside  sealed  slates. 

On  the  basis  of  these  experiments  Zollner  wrote  a 
volume  on  "  Transcendental  Physics  "  to  prove  the 
existence  of  another  world  in  the  fourth  dimension. 
But  when  Slade  tried  his  tricks  in  London  he  was 
caught  at  them  by  Professor  E.  Ray  Lankester.  He 
was  convicted  of  deception  with  intent  to  defraud  in 
the  Bow  Street  Police  Court  and  sentenced  to  three 
months'  imprisonment  with  hard  labor.  Nowadays  the 
apparatus  for  Slade's  famous  slate-writing  trick  can 
be  purchased  at  any  conjurer's  shop. 

It  is  vain  to  expect  anything  scientific  to  come  out 
of  the  seance  room  where  the  alleged  phenomena  are 
not  reproducible  under  specified  conditions  but  appear 
only  occasionally  and  under  circumstances  prescribed 
by  the  medium  who  always  may  be  and  often  is  proved 
to  be  a  sleight-of-hand — or  sleight-of-f oot — performer. 
The  fourth  dimension  which  Einstein  and  other  scien- 


SOME  SIMPLE  EXAMPLES  61 

lists  are  now  considering  is  not  conceived  of  as  the 
abode  of  departed  spirits,  a  spare  room  for  ghostly  visi- 
tants, but  merely  as  a  new  factor  in  a  mathematical 
formula.  It  offers  us  no  hope  of  ever  being  able  to 
take  coin  out  of  a  closed  safe  or  put  coin  into  an  un- 
opened coconut  but  it  does  promise  to  explain  certain 
optical  phenomena  which,  though  rare  and  minute,  are 
yet  open  to  the  observation  of  anybody,  be  he  skeptical 
or  credulous. 

SOME  SIMPLE  EXAMPLES 

Lisbon  lies  nearly  straight  east  of  New  York  but 
when  a  ship  captain  wants  to  go  to  Lisbon  he  does  not 
sail  straight  east  but  sets  his  course  a  little  northward 
in  the  beginning  and  a  litle  southward  toward  the 
end  and  so  gets  there  quicker  than  if  he  had  followed  a 
line  of  latitude.  Draw  his  course  on  a  flat  map  and  you 
would  think  he  was  taking  a  roundabout  route,  but 
trace  it  on  a  globe  and  you  will  see  that  he  is  following 
a  great  circle,  the  geodetic  line,  which  is  the  shortest 
distance  between  any  two  points  on  the  earth's  surface. 

An  airman  looking  down  on  a  rocky,  hilly,  woody 
country  sees  it  as  a  flat  plain  and  if  he  watched  a  hunter 
returning  home  with  his  bag  of  game  would  wonder 
that  he  did  not  go  straight  instead  of  wandering  around 
in  such  an  irregular  way.  Yet  the  hunter,  being  tired, 


62  EASY  LESSONS  IN  EINSTEIN 

is  taking  what  is  for  him  the  shortest  way  home  as  he 
dodges  rocks  and  circumambulates  the  hills.  The 
easiest  way  is  the  shortest  way. 

A  river  in  its  desire  to  reach  the  sea  always  takes 
the  shortest  possible  way.  Its  meanderings  are  not 
meaningless  but  determined  by  a  law  as  rigid  as  a 
law  of  geometry,  that  is,  the  law  of  gravitation  which 
prevents  the  river  from  taking  a  short  cut  over  the  hill. 

If  you  look  at  a  landscape  over  a  heated  plain  or 
bonfire  or  through  uneven  glass  you  will  see  that  the 
image  is  distorted  and  confused  because  the  rays  of 
light  are  refracted  and  entangled  as  they  pass  through 
this  unequal  medium.  Yet  each  ray  is  going  just  as 
straight  as  it  can  toward  your  eye. 

Now  to  such  familiar  cases  where  a  ray  of  light  is 
bent  out  of  its  straight  course  by  the  uneven  density 
of  the  air  or  glass  through  which  it  passes  Einstein  has 
added  another  and  unsuspected  effect,  namely,  that 
light  is  likewise  deflected  in  passing  through  a  strong 
gravitational  field  such  as  the  vicinity  of  a  large  body 
like  the  sun. 

It  has  long  been  known  that  the  displacement  of  the 
earth  in  space  and  time  (that  is  to  say,  its  motion) 
causes  an  apparent  displacement  of  the  stars  in  space. 

The  astronomer  does  not  point  his  telescope  straight 
at  a  star.  If  he  did,  he  would  not  see  it,  for,  owing  to 


SOME  SIMPLE  EXAMPLES  63 

the  forward  motion  of  the  earth,  the  telescope  moves 
out  of  range  of  the  rays  that  otherwise  would  have 
reached  it. 

If  you  have  ever  tried  to  shoot  a  bird  on  the  wing, 
or,  better,  a  prairie-dog  from  a  train  you  will  get  the 


Everyone  knows  that  a  ray  of  light  is  bent  out  of  its  straight 
course  as  it  passes  from  the  air  into  a  denser  medium  like  water 
or  glass,  and  that  this  deflection  apparently  shifts  the  position 
of  the  object  from  which  the  light  comes.  Einstein's  theory  and 
the  British  eclipse  observations  prove,  what  was  not  known  be- 
fore, that  a  ray  of  light  as  it  passes  through  the  gravitational 
field  of  a  large  body  like  the  sun,  is  also  perceptibly  bent  out  of 
its  straight  course  and  likewise  makes  an  apparent  shift  in  the 
position  of  its  source,  the  star.— From  Black  &  Davis'  "  Practical 
Physics."  Published  by  The  Macmillan  Company. 


idea.  Or,  if  you  have  not  had  this  experience,  you 
have  doubtless  watched  the  raindrops  running  down 
a  car  window  and  have  noticed  that  when  the  rain  is 
falling  straight  down  the  drops  strike  the  pane  on  a 
slant  when  the  car  is  moving  forward.  The  faster  the 
car  moves  the  greater  the  deviation  from  the  perpen- 
dicular. If  the  train  runs  backward  the  rain-streaks 


64     EASY  LESSONS  IN  EINSTEIN 

slant  in  the  opposite  direction.  If  then  you  should  be 
asked  to  point  out  the  direction  of  the  cloud  from 
which  the  rain  is  coming  you  would — unless  you  knew 
and  made  allowance  for  the  movement  of  the  train — 
point  in  a  line  with  the  streaks  on  the  pane,  sometimes 
backward,  sometimes  forward,  but  not  straight  upward 
where  the  raincloud  really  is. 

Now  the  astronomer  is  on  a  moving  train,  the  earth, 
which  is  rushing  around  a  ring  about  186,000,000  miles 
across.  Consequently  every  star  appears  to  wabble 
around  in  a  little  ellipse  and  the  astronomer  has  to  aim 
his  telescope,  now  on  one  side,  then  on  the  other,  of 
the  real  position  of  the  star  in  order  to  bring  it  on  the 
cross-hairs  of  his  object  glass.  This  apparent  dis-^ 
placement  of  the  stars  is  known  as  "  the  aberration  of 
light"  was  explained  by  Fresnel  in  1818 — to  every- 
body's satisfaction  until  recently — on  the  assumption 
that  all  space  is  filled  with  an  immovable  medium,  the 
ether,  which  transmits  the  rays  of  light  in  straight 
lines  in  the  form  of  wave  motion,  and  that  the  earth 
moves  through  the  ether  without  displacing  it,  some- 
what as  an  airplane  moves  through  still  air.  But  the 
aviator  knows  how  fast  he  is  moving  by  the  current 
of  air  streaming  back  in  his  face.  Why  then,  since  the 
ether  is  in  perfect  repose,  could  we  not  determine  the 
absolute  motion  of  the  earth  through  space  by  measur- 


THE  ECLIPSE  OBSERVATIONS  65 

ing  the  drift  of  the  ether  as  it  streams  through  the  pores 
of  the  earth?  Light  appears  to  afford  us  a  means  of 
measuring  such  a  drift  of  the  ether  through  matter,  if 
there  be  such.  Since  light  is  conveyed  by  the  ether  we 
should  naturally  expect  it  to  take  less  time  to  travel  a 
certain  distance  if  the  receiving  instrument  is  carried 
toward  the  source  of  the  light  by  the  earth  motion  than 
if  it  is  being  carried  away  from  it.  This  question  was 
put  to  the  crucial  test  by  two  American  physicists, 
Michelson  and  Morley,  who  devised  an  instrument  so 
delicate  that  it  could  detect  differences  of  one-2  5,000,- 
oooth  of  an  inch  in  the  path  of  a  light  ray.  But  al- 
though this  delicacy  was  ten  times  greater  than  was 
necessary  to  detect  the  ether  drift,  if  there  were  any, 
no  evidence  of  such  drift  could  be  discovered. 


THE  ECLIPSE   OBSERVATIONS 

In  the  history  of  science  the  year  1919  is  likely  to 
be  known,  not  as  the  year  of  the  overthrow  of  the 
German  Empire,  but  as  the  year  of  the  overthrow 
of  Newton's  law  of  gravitation.  The  British  astrono- 
mers who  went  to  Africa  to  observe  the  eclipse  of  the 
sun  May  29,  1919,  came  back  with  the  proof  that 
a  ray  of  light  passing  close  by  the  sun  is  bent  out  of 
its  straight  course.  The  photographs  taken  during  the 


66  EASY  LESSONS  IN  EINSTEIN 

six  minutes  when  the  sun  was  shadowed  show  the 
surrounding  stars  in  different  positions  from  where 
they  are  seen  when  the  sun's  disk  is  not  in  their  midst. 
This  is  the  second  time  that  Einstein  has  scored  over 
Newton.  The  first  was  in  regard  to  the  orbit  of  Mer- 
cury. If  the  sun  and  Mercury  were  alone  in  the  uni- 
verse the  planet,  according  to  Newton's  law,  would 
revolve  forever  around  the  sun  in  the  same  elliptical 
track.  But  the  presence  of  the  other  planets  makes 
Mercury  deviate  from  this  regular  route  so  the  ellipse 
it  describes  is  never  quite  the  same  but  slowly  shifts 
around  so  that  in  the  course  of  centuries  its  longer 
diameter  would  be  pointing  in  a  different  direction. 
Calculating  by  Newton's  law,  the  influence  exerted  by 
the  other  planets  astronomers  found  that  it  would  shift 
the  orbit  of  Mercury  532  seconds  of  arc  in  a  century. 
But  when  they  took  observations  on  Mercury  they 
found  that  its  orbit  was  shifting  at  the  rate  of  574 
seconds.  The  discrepancy  between  observation  and 
theory,  42  seconds,  is  thirty  times  greater  than  could 
be  accounted  for  by  errors  of  instruments  or  observa- 
tion. But  according  to  Einstein's  theory,  if  the  sun 
and  Mercury  were  alone  in  space  with  no  other  planets 
interfering,  the  orbit  of  Mercury  would  not  remain  the 
same,  but  would  advance  at  the  rate  of  43  seconds  a 
century.  This,  as  the  reader  will  observe,  is  in  sub- 


THE  PRESSURE  OF  LIGHT  67 

stantial  agreement  with  the  discrepancy  which  has  for 
two  centuries  puzzled  astronomers,  since  it  was  in- 
explicable on  the  Newtonian  theory. 

The  electro-magnetic  theory  of  light,  thought  out  by 
Clerk  Maxwell  forty-five  years  ago,  has  proved  to  be 
an  excellent  guide  to  research  and  led  to  many  practical 
applications,  such  as  wireless  telegraphy.  According  to 
this  theory  the  miles-long  Marconi  waves,  the  infinites- 
imal waves  that  we  feel  as  heat  or  see  as  light  and  the 
still  more  minute  waves  of  the  X-rays  are  movements 
of  the  same  sort,  though  differing  in  length,  and  all 
travel  at  the  same  speed  in  space  of  186,000  miles  a 
second.  It  was  one  of  the  implications  of  Maxwell's 
theory,  though  it  was  not  perceived  until  later,  that 
light  and  all  such  waves  must  exercise  a  certain  pres- 
sure upon  a  body  against  which  they  strike,  just  as  a 
jet  of  water  from  a  fireman's  hose  pushes  against  the 
side  of  a  house.  The  pressure  of  light  is  so  exceedingly 
slight  that  it  had  never  been  noticed,  but  it  has  beerl 
actually  detected  and  measured  by  Professors  E.  F. 
Nichols  of  Yale  and  G.  F.  Hull  of  Dartmouth.  The 
sunshine  falls  upon  the  earth  with  a  force  of  160  tons. 
Both  theory  and  experiment  have  shown  that  a  beam  of 
light  has  inertia  or  mass,  that  is  to  say,  a  beam  of  light 
pushes  like  a  water  jet,  and  it  has  now  been  proved, 
by  the  eclipse  expedition,  that  the  pull  of  gravity  de- 


68  EASY  LESSONS  IN  EINSTEIN 

fleets  a  beam  of  light  as  it  does  a  water  jet.  That  is 
to  say,  a  beam  of  light  has  weight,  is  attracted  by 
gravity.  This  deflection  of  a  beam  of  light  by  gravity 
is  extremely  small,  but  photographs  taken  during  the 
recent  total  eclipse  of  the  sun  show  that  star  beams 
that  passed  near  the  sun  are  bent  out  of  a  straight  path. 
A  better  illustration  of  the  eclipse  observation  than 


STRAIGHT  COURSE  OF  RAY 
.IF  SUN  HAD  NOT  BENT  IT 


_  APPARENT  SHirriN. 


STA* 


The  eclipse  expedition  found  that  the  stars  seen  about  the  sun 
appear  slightly  shifted  from  the  positions  they  occupy  on  a  map 
of  the  same  region  of  the  sky  when  the  sun  is  not  in  their  midst. 
This  shows  that  a  ray  from  a  star  is  refracted  or  bent  as  it  passes 
close  to  the  sun  and  confirms  Einstein's  theory  that  light  is  af- 
fected by  gravitation.  The  observed  angle  of  deflection  agrees 
closely  with  that  predicted  by  Einstein  but  is  twice  as  great  as 
that  required  by  Newton's  theory  of  gravitation.  In  this  dia- 
gram of  course  the  angle  of  the  deflected  ray  and  the  size  of 
the  sun  and  earth  relative  to  distance  are  greatly  exaggerated. 

I  could  word  is  given  by  Sir  Oliver  Lodge  in  his  in- 
teresting article  on  "  The  New  Theory  of  Gravitation  " 
in  The  Nineteenth  Century  of  December,  1915,  from 
which  I  therefore  quote : 

Take  a  fine  silk  thread  of  indefinite  length,  and  stretch 
it  straight  over  the  surface  of  a  smooth  table  or  floor. 
Imagine  a  star  at  one  end  of  the  thread,  and  an  eye  at  the 
other ;  and  let  the  thread  typify  one  of  the  rays  of  light 


THE  ECLIPSE  OBSERVATIONS  69 

emitted  in  all  directions  by  the  star,  viz.  the  ray  emitted 
in  the  direction  of  the  observing  eye. 

Now  take  a  halfpenny  [or  an  American  quarter,]  place 
it  on  the  table  close  to  the  thread,  so  that  the  eye  end  of 
the  thread  is  ten  feet  away ;  and  then  push  the  halfpenny 
gently  forward,  till  it  has  displaced  the  thread  the  barely 
perceptible  amount  of  one  thousandth  of  an  inch.  The 
eye  looking  along  the  thread  will  now  see  that  the  ray  is 
no  longer  absolutely  straight;  in  other  words,  the  star 
whose  apparent  position  is  determined  by  that  ray  will 
appear  slightly  shifted.  The  scale  is  fixed  by  the  size  of 
the  halfpenny,  whose  diameter,  one  inch,  is  used  to  repre- 
sent the  Sun's  diameter  of  800,000  miles.  The  ten- foot 
distance  between  eye  and  Sun  practically  supposes  that 
the  eye  is  on  the  Earth,  which  would  be  a  spot  one  hun- 
dredth of  an  inch  in  diameter,  or  about  the  size  of  this 
full  stop. 

As  for  the  distance  of  the  star,  at  the  other  far  end  of 
the  thread,  that  does  not  matter  in  the  least :  but,  on  this 
scale,  it  may  be  interesting  to  note  that  one  of  the  nearest 
stars,  about  eight  light-years  away,  would  require  the 
thread  to  be  a  thousand  miles  long. 

The  ray  is  now  bent  or  deflected  as  it  passes  the  neigh- 
borhood of  the  Sun  on  its  long  journey,  so  that  it  is  out 
of  place  one  thousandth  of  an  inch  at  a  distance  of  ten 
feet ;  and  the  effect  of  this  tilt  of  the  ray,  upon  the  ob- 
server, is  to  make  him  just  able  to  see  a  star  upon  the 
Sun's  '  limb '  when  it  is  really  behind  it,  or  to  make  him 
see  a  star  slightly  further  off  the  '  limb '  or  rim  of  the 
Sun  than  it  really  is.  The  shift  of  one  thousandth  of 
an  inch  at  a  distance  of  ten  feet  corresponds  to  an  angle 
of  one  and  three-quarter  seconds  of  arc,  which  is  just  the 


70  EASY  LESSONS  IN  EINSTEIN 

optical  shift  that  actually  ought  to  occur,  according  to 
Einstein,  when  a  ray  from  a  star  nearly  grazes  the  Sun's 
limb  on  its  way  to  a  telescope ;  and  this  is  the  optical  shift 
which  we  now  know  does  occur.  That  may  be  taken  as 
the  definite  result  of  the  recent  eclipse  observations.  The 
effect,  both  in  magnitude  and  direction,  had  been  pre- 
dicted four  years  before,  on  the  strength  of  a  mathemati- 
cal investigation,  by  Professor  Einstein. 

The  images  of  two  stars,  one  on  each  side  of  the 
sun's  disk,  will  apparently  be  crowded  a  little  apart 
when  the  sun  comes  between  them.  A  star  that  would 
be  just  eclipsed  by  the  edge  of  the  sun's  disk  if  its 
rays  came  straight  may  still  be  visible  since  the  rays  are 
curved.  In  other  words  we  can  "  see  around  a  corner  " 
as  every  good  teacher  is  said  to  do.  If  the  sun  were  en- 
circled by  a  ring  of  stars,  or  a  nebula,  like  a  halo,  the 
circle  of  light  would  be  contracted  as  it  passed  the  sun 
and  would  come  to  a  focus  at  a  place  seventeen  times 
the  distance  of  Neptune,  or  47,600,000,000  miles  be- 
yond the  sun. 

The  observations  made  by  the  British  expeditions 
during  the  eclipse  of  May  29,  1919,  were  not  altogether 
satisfactory.  At  Principe,  on  account  of  a  cloud  that 
drifted  by  at  an  inopportune  time,  only  a  few  photo- 
graphs could  be  obtained.  At  Sobral  one  of  the  object 
glasses  gave  distorted  plates,  but  the  other  gave  a  very 
good  series  of  seven  star  images.  These  when  meas- 


THE  ECLIPSE  OBSERVATIONS  71 

tired  at  the  Greenwich  Observatory  gave  the  following 
figures  which  are  in  accordance  with  those  calculated 
by  Einstein's  formual : 

RADIAL  DISPLACEMENT  OF  STARS  IN  SECONDS  OF  ANGLE 

As  observed  by  the  British  astronomers : 

.20       .32        .56       .54        .84       .97     1.02 

As  predicted  by  Einstein: 

.32        .33        40       .53        75        .85        .88 

This  is  regarded  by  the  astronomers  of  the  British 
Eclipse  Expedition  as  sufficiently  close  to  confirm  Ein- 
stein's law  but  those  who  hesitate  to  accept  so  far- 
reaching  and  subversive  a  theory  on  the  basis  of  these 
few  minute  measurements  may  hold  their  judgment  in 
suspense  until  1922  when  the  next  solar  eclipse,  visible 
in  Australia,  takes  place.  Or  possibly  some  means  may 
be  found  to  take  star  photographs  close  to  the  sun  while 
shining.  Our  California  mountain  observatories  may 
be  of  service  in  this  since  they  are  perched  above  much 
of  the  dust  and  mist  and  denser  air  that  cause  a  strong 
light  to  irradiate  and  fog  the  photographic  plate. 
Doubtless,  too,  the  old  photographs  of  earlier  eclipses 
will  now  be  got  out  to  see  if  they  contain  any  stars  suit- 
able for  measuring. 

Some  of  the  opponents  of  Einstein  suggest  that  the 
observed  deflection  of  the  starlight  may  be  due  to  a 
solar  atmosphere  that  refracts  the  rays  like  our  earthly 
air.  But  it  is  hardly  probable  that  an  enveloping  at- 


72  EASY  LESSONS  IN  EINSTEIN 

mosphere  sufficiently  dense  and  so  far-extending  as  to 
produce  such  an  effect  would  have  remained  unob- 
served and  it  is  highly  improbable  that  the  density  of 
such  an  atmosphere  should  have  just  the  density  and 
decrease  with  the  distance  at  just  the  rate  to  produce 
the  deflection  predicted  by  Einstein's  calculation.* 

The  discovery  is  rather  disconcerting  to  astrono- 
mers, for  all  their  calculations  for  the  last  three  hun- 
dred years  have  been  based  upon  the  assumption  that 
light  travels  in  straight  lines  at  even  speed  through 
empty  space  or,  what  is  the  same  thing,  through  the 
ether.  If  now  light  is  pulled  aside  by  gravitation  as  it 
goes  by  a  solid  body  the  rays  from  a  distant  star  having 
to  pass  through  the  tangled  throng  of  the  Milky  Way 
might  travel  a  very  devious  route  and  the  star  would 
appear  to  us  to  be  located  in  a  different  place  from 
where  it  really  is.  In  fact  it  is  possible  that  a  star 

*If  you  insist  upon  seeing  just  what  is  the  difference  between 
Einstein's  and  Newton's  laws  of  gravitation  here  it  is  as  given 
in  The  Scientific  Monthly  of  January,  1920: 

Any  particle  or  light  pulse  moves  so  that  the  integral  of  ds 
between  the  two  points  of  its  path  (in  four  dimensions)  is 
stationary  where 

(according  to  Einstein) 


or  (according  to  Newton) 


These  expressions  are  in  polar  coordinates  for  a  particle  of 
gravitational  mass  m. 

The  new  factor  introduced  by  Einstein  is,  as  shown  above, 

i 


THE  ECLIPSE  OBSERVATIONS  73 

which  we  see  double  may  actually  be  single  but  that 
rays  starting  out  from  it  in  different  directions  may  be 
so  deflected  by  passing  near  other  stars  that  when  they 
reach  us  they  appear  to  come  from  different  points  of 
space  and  so  appear  to  us  as  twin  stars.  There  may, 
too,  be  dead  or  dark  stars  on  the  way  whose  existence 
we  cannot  discern  and  allow  for. 

Now  those  of  us  who  are  not  astronomers  .are  not 
much  concerned  over  a  discrepancy  of  a  few  hun- 
dredths  of  a  second  in  the  measurement  of  an  angle 
by  the  telescope.  We  do  not  care  much  where  Mercury 
will  be  five  centuries  hence,  for  we  do  not  know  quite 
where  it  is  now.  If  astronomers  made  the  laws  of 
Nature  instead  of  merely  discovering  them  we  might  be 
afraid  that  at  their  next  congress  they  might  repeal 
Newton's  law  of  gravitation  and  send  us  all  flying  off 
into  space.  But  fortunately  they  have  no  such  power 
and  even  though  they  should  all  become  adherents  of 
Einstein's  most  revolutionary  theories,  Newton's  laws 
of  mechanics  and  Euclid's  laws  of  geometry  would 
remain  as  true  as  they  ever  were,  not  perhaps  absolutely 
and  universally  true,  as  we  have  assumed,  but  suffi- 
ciently accurate  for  all  practical  purposes.  Deviations 
from  them  can  only  become  detectable  when  we  come 
to  consider  movements  as  swift  as  light  waves  or  elec- 
trons. 


74  EASY  LESSONS  IN  EINSTEIN 

How  a  heavy  object  can  alter  space  relations  may 
be  seen  from  this  simple  illustration:  Stretch  a  sheet 
of  rubber  over  a  hoop  like  a  drumhead.  It  is  now 
level  and  flat  and  if  parallel  lines  are  drawn  across 
it  in  two  directions  so  as  to  divide  it  up  into  squares 
like  a  checkerboard  all  these  lines  are  straight  and 
equidistant  and  all  the  squares  are  of  equal  size. 

A  row  of  worms,  starting  in  an  even  rank  and 
crawling  along  the  parallel  lines  across  the  drumhead, 
would  keep  even  all  the  way.  Now  lay  a  bullet  on  the 
center  of  the  drumhead.  The  rubber  sags  down  and 
stretches,  most  in  the  middle,  least  at  the  edges.  The 
"  parallel "  lines  are  no  longer  equidistant  The 
squares  are  no  longer  equal.  The  lines  are  no  longer 
of  the  same  length.  If  now  we  repeat  our  worm  race 
we  shall  find  that  those  worms  following  lines  close 
to  the  weight  have  to  go  down  hill  and  up  again  and 
so  travel  a  greater  distance  to  traverse  the  same  num- 
ber of  squares  than  those  following  lines  nearer  the 
edge  which  lie  comparatively  flat  and  are  nearly  as 
short  as  before.  Consequently  the  worms  will  be 
slowed  up  in  proportion  to  their  nearness  to  the  center 
and  the  row  of  their  heads  will  be  swung  around  at 
an  angle  to  their  former  frontage. 

We  might  "explain"  this  by  assuming  that  the 
worms  on  seeing  the  bullet  to  one  side  were  drawn 


A  CHOICE  OF  EXPLANATIONS  75 

by  their  curiosity  a  little  toward  it,  those  nearest  of 
course  being  drawn  the  most.  Or  if  we  had  got  be- 
yond this  crude  animistic  method  of  explanation  we 
might  assume  that  the  bullet  was  attached  to  the  head 
of  each  worm  by  an  invisible  lariat  which  being  pulled 
by  the  bullet  drew  the  worms  more  or  less  to  one  side, 
the  shorter  the  lariat  the  stronger  the  pull.  Or  if  we 
had  outgrown  this  crude  mechanical  method  of  ex- 
planation we  might  assume  the  existence  of  a  "  force  " 
in  the  lead  which  in  some  mysterious  manner  attracts 
the  heads  of  the  worms  inversely  as  the  square  of  their 
distance.  But  instead  of  inventing  a  wormhead  psy- 
chology or  an  invisible  cord  or  an  incomprehensible 
force  is  it  not  simpler  to  consider  the  space  between 
and  to  suppose  that  the  lines  to  be  traversed  are  length- 
ened in  the  neighborhood  of  the  weight? 

Now  these  four  successive  methods  of  explanation 
have  been  used  to  account  for  gravitation.  First  it 
was  assumed  by  the  ancient  Babylonians  and  Hebrews 
that  the  sun  and  stars  were  living  beings,  gods  or 
angels,  moving  of  their  own  volition  around  the  earth, 
or  at  least  that  each  was  guided  in  its  orbit  by  its 
particular  god  or  angel.  The  later  Greeks  of  Ptolemy's 
time  supposed  the  heavenly  bodies  to  be  set  in  con- 
centric crystal  spheres  and  so  revolved;  I  presume  by 
somebody  turning  a  crank  behind  the  scenes.  Then 


76  EASY  LESSONS  IN  EINSTEIN 

came  Newton  and  said :  "  Let's  discard  the  Ptolemaic 
spheres  and  all  mechanical  connection  and  assume  a 
force  of  gravitation  attracting  all  bodies  in  propor- 
tion to  their  masses  and  inversely  proportional  to  the 
squares  of  the  distances  separating  them."  Now  comes 
Einstein  and  says :  "  Let's  discard  this  hypothetical 
force  and  simply  assume  that  the  field  of  time  and  space 
"traversed  by  a  moving  body  is  altered  if  there  is  an- 
other body  in  the  vicinity."  In  Einstein's  view  gravi- 
tation is  not  a  force;  it  is  a  distortion  of  space  and 
time  in  the  presence  of  matter.  A  comet  sweeping 
past  the  sun  cannot  pursue  a  straight  course,  as  it  could 
in  interstellar  space,  but  follows  a  curved  path  about 
the  sun  which  is  for  the  comet  the  shortest  way  it  can 
go  under  the  circumstances. 

So,  too,  a  row  of  light  waves  coming  from  a  dis-* 
tant  star  keeps  an  even  front  as  they  pass  through 
empty  space  but  as  they  come  close  to  the  sun  they 
find  their  paths  impeded,  or,  we  may  say,  stretched. 
Those  going  nearest  the  sun  are  slowed  up  the  most ; 
those  farthest  off  the  least.  Consequently  the  wave- 
front  is  slued  around  a  bit  and  the  direction  of  the 
ray  is  slightly  altered. 

If  now  light  waves  have  difficulty  getting  past  the 
sun  we  should  expect  that  they  would  experience  like 
difficulty  getting  away  from  the  sun.  They  would  be 


SIR  OLIVER  LODGE'S  OPINION  77 

slowed  up  a  bit  by  its  gravitational  pullback.  The  fre- 
quency would  be  reduced ;  the  interval  of  time  between 
wave-crests  lengthened.  This  means,  in  the  case  of 
sound,  lowering  the  pitch.  Touch  your  finger  to  the 
turntable  of  your  phonograph  and  you  flat  the  tone. 
In  the  case  of  light,  it  means  change  of  color  toward 
the  red.  This  effect,  according  to  Einstein,  should  be, 
but  has  not  been,  observed. 

"If  Einstein's  third  prediction  is  verified/'  saya  Sir 
Oliver  Lodge,  "  Einstein's  theory  will  dominate  all 
higher  physics  and  the  next  generation  of  mathemati- 
cal physicists  will  have  a  terrible  time  of  it.  For  uni- 
versity courses  and  for  all  practical  purposes  we  shall 
have  the  Galilean  and  Newtonian  dynamics  but  they 
will  reign  as  a  limited  monarchy  and  sooner  or  later 
the  Einstein  physics  cannot  fail  to  influence  every  in- 
telligent man.  If  these  complications  are  to  come  into 
science  we  must  leave  them  to  the  younger  men.  I 
hope  that  gravitation,  now  that  it  has  begun  to  inter- 
act with  light,  will  begin  to  give  up  its  secrets,  but  in 
my  time  I  must  be  content  to  get  secrets  out  dynami- 
cally and  leave  transcendental  methods  to  others." 

One  English  scientist,  Thomas  Case,  writes  to  The 
Times  to  protest  that  it  would  have  been  in  much  better 
taste  for  the  Royal  Society  to  have  adjourned  its  dis- 
cussion "  before  bringing  into  question  the  reputation 


78     EASY  LESSONS  IN  EINSTEIN 

of  Newton,  who  was  President  of  the  Royal  Society 
for  the  last  twenty-five  years  of  his  life  and  raised  the 
society  to  the  acme  of  its  fame." 

WHO   IS   EINSTEIN? 

Albert  Einstein  was  born  in  Germany  in  1874. 
He  early  showed  the  bent  of  his  genius  and  at  the 
age  of  twelve,  when  his  fellow  pupils  were  plodding 
along  with  their  daily  tasks,  he  was  plunging  through 
works  of  higher  mathematics  borrowed  from  his 
teacher.  He  was  only  eighteen  when  he  conceived  the 
outlines  of  his  theory  and  ten  years  later  it  was  ready 
to  give  to  the  world.  He  left  Germany  for  Switzer- 
land at  the  age  of  sixteen  and  became  naturalized  as  a 
Swiss  citizen.  His  first  academic  position  was  the 
Professorship  of  Mathematical  Physics  at  the  Zurich 
Polytechnic.  Then  the  founding  of  the  Kaiser  Wil- 
helm  Academy  for  Research  at  Berlin  gave  him  oppor- 
tunity to  work  out  his  theories  undisturbed  by  other 
duties.  Shortly  before  the  war  he  was  called  to  Berlin 
to  succeed  the  famous  Dutch  physicist,  Professor  van't 
Hoff  in  the  Academy.  The  object  of  this  institution 
was  the  same  as  Carnegie  had  when  he  founded  his 
institution  for  scientific  research  at  Washington,  which 
was  to  seek  out  the  exceptional  man  wherever  he  may 


WHO  IS  EINSTEIN?  79 

be  found  and  set  him  at  his  peculiar  tasks.  At  Berlin 
Einstein  receives  a  salary  of  $4,500  and  has  nothing  to 
do  but  sit  and  think.  This  he  continued  to  do  all 
through  the  five  years  of  war  and  revolution  as  quietly 
and  persistently  as  Kant  at  Konigsberg  during  the 
wars  and  revolutions  of  a  century  before.  Or  as 
Archimedes  at  the  siege  of  Syracuse  who  was  absorbed 
in  drawing  geometrical  figures  in  the  sand — his  black- 
board— when  a  Roman  soldier  ran  him  through  with 
a  spear.  On  two  occasions  he  took  part  in  the  world- 
struggle  going  on  about  his  study,  both  actions  greatly 
to  his  credit.  In  the  beginning  he  refused  to  sign  the 
manifesto  of  the  German  men  of  science  denying  all 
the  charges  against  Germany,  and  at  the  time  of  the 
armistice  he  signed  an  appeal  in  favor  of  the  revolu- 
tion. He  is  an  ardent  Zionist  and  has  promised  to 
aid  the  Hebrew  university  which  is  to  be  founded  at 
Jerusalem. 

According  to  tradition,  Isaac  Newton  was  led  to  his 
theory  of  gravitation  by  observing  an  apple  falling 
from  a  tree  in  his  garden.  The  newspaper  corre- 
spondents start  a  similar  tradition  by  reporting  that 
Einstein  got  his  theory  of  gravitation  by  observing  a 
man  falling  from  the  roof  of  a  building  in  Berlin. 
Now  a  man  has  the  advantage  of  an  apple  in  that  he 
is  able  to  tell  his  sensations.  When  Dr.  Einstein,  who 


80  EASY  LESSONS  IN  EINSTEIN 

had  seen  the  accident  from  his  library  window  in  the 
top  story  of  a  neighboring  apartment  house,  reached 
the  spot  he  found  the  man  had  hit  upon  a  pile  of  soft 
rubbish  and  had  escaped  almost  without  injury.  Asked 
how  it  felt  to  fall  he  told  Dr.  Einstein  that  he  had  no 
sensation  of  downward  pull  at  all.  This  led  Dr.  Ein- 
stein to  consider  whether  the  relativity  theory,  which  he 
had  applied  only  to  the  case  of  uniform  motion  in  a 
straight  line,  could  not  be  extended  to  difform  or  ac- 
celerated motion  by  gravitation.  So  the  special  rela- 
tivity theory  which  he  had  enunciated  in  1905  devel- 
oped ten  years  later  into  a  generalized  relativity  theory 
(  Verallgemeinerte  Relativitatstheorie) . 

HOW    TO     LOSE    WEIGHT 

A  man  falling  out  of  an  airplane  is  obeying  a  natu- 
ral impulse,  namely,  the  force  of  gravitation.  So  long 
as  he  does  not  resist  he  is  free  as  air,  light  as  a  feather, 
and  altogether  comfortable.  He  can  look  down  with 
complacency  and  contempt  on  the  poor  mortals  below 
him  who  are  trying  to  stand  up  against  this  natural 
impulse  and  laboriously  dragging  one  foot  after  an- 
other as  they  crawl  about  the  earth  when  they  might 
be  flying  through  space  without  effort  as  he  is.  It  is 
only  when  he  tries  to  stop  his  free  fall  by  bumping 


HOW  TO  LOSE  WEIGHT  81 

against  the  ground  that  he  gets  into  trouble  on  ac- 
count of  gravitation.  It  was  in  this  way  that  the  Cal- 
vinists,  who  were  a  sort  of  mathematical  theologians, 
conceived  of  the  fall  of  man.  The  sinner  is  simply 
obeying  the  force  of  natural  depravity,  namely,  moral 
gravity,  and  so  long  as  he  is  conscienceless  and  does 
not  consider  his  inevitable  end  he  has  no  knowledge 
of  the  moral  law  and  is  quite  happy  in  his  down- 
fall. 

A  person  falling  freely  loses  all  his  weight.  His 
hat  does  not  press  down  on  his  head.  His  feet  do  not 
press  down  on  his  shoes.  If  he  lets*  go  of  his  walking- 
stick  it  does  not  "  fall  down  "  at  his  feet.  It  stands 
upright  and  simply  travels  along  with  him.  For,  as 
Galileo  showed  when  he  dropped  his  big  and  little 
cannon  ball  off  the  Leaning  Tower  of  Pisa,  all  bodies 
fall  with  the  same  speed. 

If  he  were  in  a  falling  elevator  with  an  opaque  door 
he  would  not  know  he  were  falling  unless  he  surmised 
it  from  the  absence  of  gravitation  as  evidenced  by  his 
own  feeling  of  lost  weight  and  the  queer  behavior  of 
the  objects  in  the  car.  He  might  fall  all  his  life  and 
never  find  it  out.  The  law  of  gravitation  is  like  crim- 
inal law;  you  don't  feel  it  till  you  come  into  conflict 
with  it. 

Or  if  our  illustration  requires  too  tall  a  skyscraper, 


82  EASY  LESSONS  IN  EINSTEIN 

let  us  imagine  that  a  comet  as  it  flies  by  knocks  a  chip 
off  the  earth  with  a  group  of  people  on  it.  This  ter- 
restrial fragment,  cast  loose  in  space,  gets  caught  by 
the  attractive  force  of  some  gigantic  and  distant  star 
and  falls  toward  it  with  ever-increasing  velocity  for 
thousands  of  years.  The  inhabitants  of  this  errant  orb 
would  never  know  it  from  their  own  feelings  or  any 
observations  they  could  make  on  their  own  little  world. 
Does  that  seem  incredible  to  you?  Then  tell  me  how 
do  you  know  but  this  our  world  is  such  a  planet  and 
together  with  the  solar  system  has  been  falling  for 
thousands  of  years  toward  some  center  of  attraction? 
Astronomers,  indeed,  say  that  we  are  moving  at  tre- 
mendous speed  toward  Canis  Major,  in  other  words 
that  the  world  is  going  to  the  dogs. 

All  this  means  that  uniformly  accelerated  motion, 
such  as  gravitation  imparts  to  a  freely  falling  body, 
is,  like  uniform  translatory  motion,  a  question  of  rela- 
tivity and  cannot  be  discovered  by  an  observer  carried 
along  by  such  movement 

The  idea  that  uniform  translation,  like  the  moving 
train  we  have  considered,  is  merely  relative  motion,  is 
an  old  idea  and  not  hard  to  understand  or  accept.  But 
when  we  try  to  extend  the  principle  of  relativity  to 
acceleration,  that  is,  to  a  rate  of  motion  that  is  con- 
tinuously increased  or  retarded,  we  get  a  new  and  revo- 


A  SUBSTITUTE  FOR  GRAVITY  83 

lutionary  conception  of  the  universe  and  are  drawn 
into  some  very  startling  conclusions.  Einstein  took 
this  step  five  years  ago  and  that  is  what  has  caused  the 
present  excitement.  For  Einstein  when  he  once  gets 
hold  of  an  idea  follows  it  wherever  it  leads  him  with 
the  undaunted  determination  of  a  Nantucket  sailor 
towed  by  a  harpooned  whale.  It  was  a  whale  of  an 
idea  that  he  harpooned  in  1915  and  it  carried  him  into 
strange  waters.  It  led  directly  to  a  contradiction  or 
correction  of  one  of  the  two  fundamental  postulates 
which  he  had  laid  down  as  the  foundation  of  his 
theory  of  the  universe  in  1905,  namely,  that  the  veloc- 
ity of  light  in  space  is  a  constant.  But  he  promptly 
abandoned  this  idea  with  cheerful  nonchalance  in  favor 
of  the  new  notion  that  the  velocity  of  light  is  affected 
by  gravitation.  <, 

A   SUBSTITUTE   FOR   GRAVITY 

Let  us  then  follow  Einstein  and  apply  his  Principle 
of  Equivalence  to  accelerated  motion  and  see  what  it 
leads  to.  Imagine  yourself  shut  up  inside  a  closed 
chamber,  like  an  elevator  car,  somewhere  out  in  space 
away  from  the  gravitational  forces  of  the  earth  or  sun. 
Suppose  this  chamber  to  be  rising  with  a  constantly 
increasing  velocity.  We  can,  if  we  want  to  be  definite 


84     EASY  LESSONS  IN  EINSTEIN 

about  it,  assume  that  the  chamber  is  a  big  shell  pulled 
up  by  a  cable  coiling  around  a  conical  windlass  that 
hauls  it  up  faster  all  the  time.  Or  we  can  assume  that 
it  is  propelled  from  behind  by  the  continuous  backfire 
of  explosives,  like  the  rocket  which  Professor  Goddard 
proposes  to  send  to  the  moon.  All  we  need  is  some 
force,  not  gravitation,  capable  of  giving  the  chamber 
every  second  an  additional  velocity  of  thirty-two  feet 
a  second.  Now  the  point  is  that  if  you  were  in  such 
an  upward-moving  chamber  you  would  not  know  but 
what  you  were  resting  on  the  earth.  Everything  would 
behave  exactly  the  same.  If  you  now  weigh  one  hun- 
dred and  fifty  pounds  on  the  scales,  that  is,  if  your 
shoe  soles  press  down  with  that  force,  the  floor  of 
the  rising  chamber  would  press  upward  with  that  same 
force  and  you  would  not  know  the  difference.  If 
you  let  loose  a  ball  from  your  hand  the  floor  would 
rise  up  to  meet  it  and  it  would  appear  to  fall.  If  you 
threw  the  ball  upward  with  a  velocity  greater  than 
the  velocity  of  the  chamber  at  the  moment,  the  ball 
would  rise,  but  since  the  velocity  of  the  chamber  was 
constantly  increasing  the  floor  would  gain  on  the  ball 
and  catch  up  with  it.  This  would  look  to  you  just 
the  same  as  when  on  earth  you  threw  a  ball  into  the 
air  and  it  fell  back  to  the  ground,  drawn,  as  you  are 
accustomed  to  think,  by  "  the  force  of  gravitation." 


A  SUBSTITUTE  FOR  GRAVITY  85 

But  here  we  have  no  "  force,"  but  merely  a  mode  of 
motion. 

Under  such  circumstances  it  would  seem  that  all 
Nature  conspired  to  keep  you  in  the  dark.  You  appeal 
to  the  ether,  that  supposedly  stable  and  stationary 
medium  that  fills  all  space,  but  that  also  fails  you. 
You  try  the  Michelson-Morley  experiment  to  see  if  you 
are  moving  through  the  ether  or  at  rest  on  the  earth 
but  your  apparatus  expands  or  contracts  just  enough 
to  deceive  you. 

You  now  try  observing  horizontal  rays  of  light  but 
they  seem  to  bend ;  that  is,  a  beam  of  sunshine  entering 
a  pinhole  on  one  side  of  your  camera  obscurcv  will  not 
strike  the  wall  at  a  spot  exactly  opposite  but  a  little 
below  it,  if  you  have  instruments  sufficiently  delicate  to 
show  this.  You  try  vertical  rays  of  light  in  this  fash- 
ion: You  examine  with  the  spectroscope  rays  of  light 
coming  from  two  sources  below  (behind)  your  instru- 
ment, one  at  a  distance  and  the  other  nearer.  Now 
since  you  are  moving  away  with  increasing  speed,  the 
light  from  the  farther  source  will  have  to  take  longer 
strides  to  catch  up.  Or  in  other  words,  its  frequency 
will  be  reduced  and  it  will  be  shoved  toward  the  red 
end  of  the  spectrum  where  the  longer  waves  are.  You 
will  have  noticed  that  when  a  whistling  train  rushes 
past  the  train  you  are  on,  the  whistle  as  it  comes  to- 


86  EASY  LESSONS  IN  EINSTEIN 

ward  you  is  raised  in  pitch  (decreased  wave-length) 
and  as  it  recedes  from  you  is  lowered  in  pitch  (in- 
creased wave-length). 

Now,  says  Einstein  to  himself,  if  my  Principle  of 
Equivalence  is  correct  and  there  is  no  difference  be- 
tween (i)  weight  and  (2)  the  accelerated  upward 
movement  of  an  observer,  then  all  the  optical  effects 
that  I  have  thought  out  in  the  second  case  must  apply 
to  the  first,  that  is,  to  gravitation.  It  must  follow 
that  a  ray  of  light  passing  through  a  gravitational 
field  will  be  bent  out  of  its.  course  as  though  it  were 
attracted  by  the  heavy  body.  This  prediction  has  been 
verified.  It  must  further  follow  that  light  proceeding 
from  a  heavy  body  like  the  sun  or  a  star  will  be  held 
back  or  slowed  up  by  the  attraction  of  gravitation,  and 
the  spectral  lines  will  be  displaced  toward  the  left  as 
compared  with  the  same  lines  in  the  spectrum  of  an 
earthly  light.  Now  such  displacement  has  been  ob- 
served in  stellar  spectra  but  it  does  not  seem  to  be  of 
the  right  value  to  satisfy  Einstein's  equation  and  it 
has  not  been  observed  in  sunlight. 

The  remarkable  thing  about  it  is  that  Einstein,  by 
following  a  line  of  reasoning  somewhat  like  that  which 
I  have  crudely  outlined,  not  merely  supplied  an  ex- 
planation for  phenomena  that  had  been  observed  but 
could  not  be  explained  (such  as  the  discrepancy  in 


MECHANICAL  VS.  MATHEMATICAL  MINDS  87 

the  orbit  of  Mercury)  but  he  provided  in  advance  the 
explanation  for  phenomena  that  had  never  been  ob- 
served until  he  directed  attention  to  it  (such  as  the 
deflection  of  starlight  by  the  sun).  Sir  Oliver  Lodge 
says  of  this:  * 

"  Before  Einstein's  prediction  nothing  of  the  kind  had 
been  seen,  nothing  of  the  kind  had  been  looked  for,  nor, 
so  far  as  it  is  known,  had  such  an  amount  of  deflection 
been  suspected. 

Whatever  may  ultimately  be  thought  of  the  validity 
of  Einstein's  views  as  a  whole  it  is  evident  that  he  has 
worked  out  a  mathematical  method  of  unprecedented 
power  and  wide  usefulness. 

Professor  Bumstead  of  Yale  says: 

Einstein's  theory  is  important  in  that  it  exemplifies  a 
method  which  is  in  many  respects  new  in  theoretical 
physics  and  which  may  prove  to  be  a  very  powerful 
method  for  advancing  scientific  knowledge.  There  was 
no  idea  that  the  prediction  of  the  bending  of  light  would 
fix  up  Mercury's  perihelion  and  incidentally  explain  a 
two-century  old  astronomical  difficulty.  That  came 
straight  out  of  a  blue  sky. 

MECHANICAL  VERSUS    MATHEMATICAL   MINDS 

We  sometimes  hear  it  said  that  "  Einstein  has  over- 
thrown Newton's  theory  of  gravitation."  That  is  im- 

*Ninte€nth  Century,  December,  1919. 


88  EASY  LESSONS  IN  EINSTEIN 

possible  because  Newton  did  not  have  any  theory  of 
gravitation.  He  merely  laid  down  the  law  of  gravita- 
tion. He  told  how  bodies  behaved  toward  their  neigh- 
bors; he  did  not  tell  why.  Newton  was  not  content 
with  the  idea  of  action  at  a  distance  through  empty 
space  and  he  tried  to  explain  gravitation  by  the  pres- 
sure of  the  ether  on  material  bodies  but  he  was  not 
satisfied  with  the  results  and  did  not  publish  them.  In 
the  234  years  since  many  men  have  tried  their  hands 
at  devising  some  sort  of  machinery  that  will  "  explain  " 
gravitation.  For  human  beings  are  like  Toddie  of 
"  Helen's  Babies  "  and  want  to  have  the  watch  opened 
so  they  can  "  see  the  wheels  go  wound."  At  least 
Anglo-Saxons  have  that  desire.  Poincare,  the  French 
physicist,  said  this  is  the  distinction  between  the  Anglo- 
Saxon  and  Latin  minds;  the  former  are  uneasy  until 
they  can  imagine  a  mechanical  model  to  represent  natu- 
ral phenomena,  the  latter  are  satisfied  with  a  mathe- 
matical formula  expressing  the  action.  The  ether, 
which  was  invented  to  explain  'light,  also  required  "  ex- 
planation/' Lord  Kelvin  imagined  it  to  consist  of  spin- 
ning tops  which  have  a  sort  of  mobile  stability.  Sir 
Oliver  Lodge  has  rilled  it  with  a  complicated  structure 
of  interlocking  geared  wheels  to  account  for  electro- 
magnetic action.  These  are  typical  Anglo-Saxon 
modes  of  thinking.  On  the  other  hand,  Einstein,  who, 


MECHANICAL  VS.  MATHEMATICAL  MINDS  89 

in  spite  of  his  Hebrew  blood  and  German  training,  has 
preeminently  what  Poincare  claims  as  the  Latin  tem- 
perament, does  not  have  any  use  for  the  ether  and  does 
not  care  at  all  whether  he  can  "  picture  "  the  fourth 
dimensions  on  paper  or  not. 

Now  some  of  us  are  excessively  Anglo-Saxon  in  our 
attitude  toward  mathematics.  It  is  with  a  fellow-feel- 
ing for  such  folks  that  I  have  filled  this  little  volume 
with  such  crude  and  absurd  analogies  as  trains  and 
elevators  and  projectiles  flying  through  space  and 
Coney  Island  mirrors.  To  the  mathematically  minded 
such  illustrations  are  not  simplifications  but  complica- 
tions, not  representations  but  caricatures.  Mathe- 
matics is  the  proper  language  of  physics  as  the  five- 
barred  staff  is  the  proper  language  of  music.  Ask 
a  musician  to  explain  a  symphony  in  plain  every- 
day English  and  he  cannot  do  it,  though  he  carry  the 
Oxford  Dictionary  in  his  head.  He  can  have  the 
music  played  for  us  or  he  can  show  us  the  printed 
score  but  he  could  never  convey  it  in  ordinary  lan- 
guage however  long  he  might  be  willing  to  talk  or 
we  to  listen.  But  we  must  not  do  the  musician  or  the 
mathematician  the  injustice  to  suspect  that  his  notions 
are  hazy  or  absurd  because  he  cannot  explain  (i.e. 
translate)  them  to  us. 

Nor  should  we  assume  that  the  new  ideas,  because 


90  EASY  LESSONS  IN  EINSTEIN 

they  are  more  difficult  for  us  to  grasp,  are  necessarily 
more  complicated  or  extravagant  than  the  old.  A 
friend  of  mine  who  is  familiar  with  both  tells  me  that 
Einstein's  papers  are  easier  reading  than  Newton's 
"  Principia." 

The  aim  of  science  is  simplification  through  generali- 
zation and  this  is  the  widest  generalization  yet  at- 
tempted. It  promises  to  bring  gravitation  into  rela- 
tionship with  other  forces.  One  great  generalization, 
the  law  of  the  conservation  of  energy  worked  out  by 
Joule  and  others  in  the  forties,  brought  heat  and  work 
and  chemical  power  all  into  one  simple  system.  Clerk 
Maxwell  in  the  seventies  brought  together  in  one  beau- 
tiful formulation  all  the  diverse  phenomena  of  light, 
electricity  and  magnetism. 

But  gravitation  has  always  stood  out  against  any 
such  league  of  natural  forces.  It  refused  to  come  into 
the  combine.  It  remained  unique,  independent,  irre- 
ducible, unalterable  and  inexplicable.  Everything  else 
is  correlated  and  interactive.  Heat  destroys  mag- 
netism, magnetism  produces  electricity;  electricity  dis- 
solves chemical  combination;  chemical  combination 
produces  heat ;  heat  causes  motion ;  motion  makes  mag- 
netism; magnetism  produces  heat;  and  so  on  in  end- 
less round,  each  affecting  all  the  others.  Different 
substances  behave  very  differently;  one  is  more  easily 


MECHANICAL  VS.  MATHEMATICAL  MINDS  91 

heated  than  another;  some  are  readily  magnetized  or 
electrified,  others  are  not  so  susceptible;  certain  ele- 
ments rush  into  each  others'  arms,  others  cannot  be 
forced  into  combination. 

But  gravitation  seemed  indifferent  to  all  these  things ; 
it  showed  no  prejudices  or  preferences.  It  attracted 
with  equal  force  all  sorts  of  substances,  no  matter 
whether  they  were  hot  or  cold,  shiny  or  black,  moving 
or  still,  electrified  or  magnetized  or  neither.  Other 
forces  and  effects  too  required  time  for  action  at  a 
distance.  Sound  travels  at  the  rate  of  1,100  feet  a 
second  in  ordinary  air.  Light  travels  at  the  rate  of 
186,337  miles  a  second  in  a  vacuum.  But  the  force  of 
gravity  seemed  not  to  require  any  time  but  to  be  every- 
where, acting  all  the  while,  and  nothing  could  shield  it 
off  or  shut  it  out  or  in  any  way  interfere  with  it.  The 
substance  or  mass  of  a  body  as  measured  by  its  weight 
(the  gravitational  pull  of  the  earth)  was  always  identi- 
cal with  its  mass  as  measured  by  its  inertia  (its  re- 
sistance to  being  set  in  motion).  All  the  energies  are 
interchangeable.  All  other  forces  could  be  reduced  or 
increased,  annulled  or  brought  into  effect  at  will.  Not 
so  gravitation.  Any  bodies  of  a  certain  mass  placed  at 
a  certain  distance  apart  are  always  drawn  by  the  same 
attraction.  That  is,  gravitation  is  affected  by  nothing 
except  geometrical  relationships. 


92  EASY  LESSONS  IN  EINSTEIN 

This  naturally  leads  us  to  suspect  that  gravitation 
is  nothing  but  a  geometrical  relationship,  that  it  is 
somehow  a  peculiarity  of  space  itself.  If  so,  our  de- 
mand of  the  physicist  that  he  show  us  gravitation, — 
drag  out  this  mysterious  force  from  its  hiding-place 
and  let  us  see  it — is  altogether  irrational.  It  is  like  a 
blind  man  hunting  in  a  dark  cellar  at  midnight  for  a 
black  cat  that  isn't  there.  The  geometrician  tells  us 
that  the  internal  angles  of  any  triangle  are  equal  to 
two  right  angles.  Shall  we  ask  him,  what  is  the  force 
that  makes  it  so?  Shall  we  refuse  to  ride  on  a  trolley 
car  until  the  electrician  can  answer  our  persistent  ques- 
tion; "  but  what  is  electricity?  "  When  we  ask  such  a 
question  we  are  really  asking  him  to  tell  us  what  elec- 
tricity is  not.  To  show  us  what  electricity  is  he  can 
keep  his  mouth  shut  and  simply  point  to  the  dynamo 
that  produces  it,  the  wire  that  conveys  it  and  the 
motor  that  consumes  it.  But  what  we  secretly  mean 
is  that  he  show  us  a  mechanical  model  that  im- 
perfectly imitates  some  of  the  actions  of  electricity 
or  a  mathematical  formula  that  will  calculate  its 
effects. 

Now  Einstein  seems  in  the  way  of  making  gravita- 
tion the  foundation  of  a  new  system  of  geometry.  In- 
stead of  "  explaining  "  gravitation  in  terms  of  some- 
thing else  he  will  explain  other  things  in  terms  of 


THE  WEIGHT  OF  LIGHT  93 

gravitation,  or  rather  of  his  space-time  manifold  of 
which  gravitation  is  one  of  the  properties. 

Einstein's  law  of  gravitation  proves  to  be  more  ac- 
curate than  Newton's  law,  but  the  correction  is  trifling 
except  in  rare  cases.  But  Einstein's  theory  of  gravita- 
tion is  fundamental  and  far-reaching  and  if  it  is  sub^ 
stantiated  it  will  revolutionize  physics  and  radically 
affect  our  ordinary  conceptions  of  the  universe.  The 
verification  of  a  prediction  does  not  necessarily  prove 
the  truth  of  the  hypothesis  that  led  to  the  prediction. 
Many  a  scientific  discovery  has  come  out  of  a  false 
assumption.  Just  as  a  miner  may  reopen  an  aban- 
doned gold  mine  or  work  over  his  dump  heap  to  get 
more  out  of  it,  so  scientists  often  return  to  an  old 
theory  which  they  had  abandoned  for  a  more  fruitful 
hypothesis. 

THE   WEIGHT  OF  LIGHT 

It  is  interesting  to  see  that  our  modern  physicists 
show  a  disposition  to  adopt  a  corpuscular  or  emission 
theory  of  light  not  unlike  the  conception  which  Newton 
steadfastly  and  vainly  defended  against  the  undula- 
tory  theory.  Professor  Thomson,  of  Cambridge,  re- 
minds us  that  the  crucial  experiment  between  the  two 
theories  was  the  test  made  by  Bennet  in  1792  to 
determine  if  light  exerted  any  pressure  on  a  body 


94  EASY  LESSONS  IN  EINSTEIN 

when  it  struck  it  as  it  would  if  light  consisted  of 
minute  particles  driven  straight  forward  with  great 
velocity.  Bennet  found  no  such  pressure  and  the  cor- 
puscular theory  was  regarded  as  disproved.  But  it 
was  later  found  that  the  undulatory  theory  also  in- 
volved such  a  pressure,  and  recent  experimenters  have 
proved  and  measured  it.  As  Professor  Thomson  says : 

It  is  perhaps  fortunate  that  Bennet  had  not  at  his 
command  more  delicate  apparatus.  Had  he  discovered 
the  pressure  of  light,  it  would  have  shaken  confidence 
in  the  undulatory  theory  and  checked  that  magnificent 
work  at  the  beginning  of  the  last  century  which  so  greatly 
increased  out  knowledge  of  optics. 

Of  course  any  modern  form  of  the  emission  theory^ 
of  light  must  account,  as  Newton's  did  not,  for  suchj 
phenomena  as  interference  and  polarization,  which  are; 
so  satisfactorily  handled  by  the  undulatory  theory. 
That  is,  it  must  combine  the  best  features  of  both. 
Professor  Thomson  shows  that  only  an  exceedingly 
small  fraction  of  the  ether  is  concerned  in  the  for- 
ward movement  of  light,  in  other  words,  "  the  wave 
front  must  be  more  analogous  to  bright  specks  on  a 
dark  ground  than  to  a  uniformly  illuminated  surface." 
He  does  not,  however,  go  so  far  as  Planck  in  regard-/ 
ing  it  as  proved  that  radiant  energy  of  all  kinds 


THE  WEIGHT  OF  LIGHT  95 

a  unit  or  atomic  structure,  the  color  of  the  light  de- 
pending on  the  size  of  these  particles. 

The  discovery  of  the  pressure  of  a  beam  of  light 
has  led  to  some  startling  conclusions.  For  example, 
what  shall  be  done  with  Newton's  law  that  action  and 
reaction  are  equal?  When  a  gun  is  fired  the  kick  of 
the  gun  is  balanced  by  the  momentum  of  the  projec- 
tile. When  a  reflector  throws  a  beam  of  light  into 
space,  the  kick  of  it  is  there  all  right  but  where  is  the 
projectile,  if  light  is  merely  the  undulation  of  an  im- 
ponderable fluid?  We  may  suppose  that  the  light 
strikes  some  dark  body  out  in  space,  transmits  its  im- 
pulse to  that  and  Newton's  laws  is  satisfied,  but  it  may 
be  a  long  time  before  such  a  body  is  encountered  and 
it  may  never  be :  at  any  rate  a  law  that  remains  in  a 
state  of  innocuous  desuetude  for  several  thousand 
years  is  not  good  for  much.  We  must  then  assume 
that  light  has  mass  since  it  has  inertia  and  momentum. 
But  if  light  has  mass  it  must  have  weight;  that  is,  it 
must  be  attracted  by  gravitation.  The  eclipse  observa- 
tions confirmed  this  deduction.  Newton  would  have 
expected  something  of  this,  for  he  says  in  his  Opticks:  * 

Query  i. — Do  not  Bodies  act  upon  Light  at  a  dis- 
tance, and  by  their  action  bend  its  Rays,  and  is  not  this 
action  (caeteris  paribus)  strongest  at  the  least  distance? 

*  Quoted  by  Eddington  in  Contemporary  Review,  December, 
1919. 


96  EASY  LESSONS  IN  EINSTEIN 

The  observed  deflection  of  light  due  to  the  sun's 
gravitation  is  greater  than  Newton  would  have  antici- 
pated but  it  would  have  been  still  more  disconcerting 
to  the  nineteenth-century  physicists,  for  in  giving  up 
Newton's  emission  theory  they  had  come  to  regard 
light  as  merely  a  form  of  motion  in  a  weightless 
medium,  the  ether.  Disembodied  energy,  like  heat  and 
light  in  ethereal  space,  was  regarded  as  having  no  mass 
or  weight.  Twentieth-century  physicists  are  coming 
to  the  opposite  view,  that  the  mass  of  a  body  is  the 
measure  of  its  internal  energy.  If  so,  mass  is  not  con- 
stant but  changes  with  composition,  temperature,  struc- 
ture, electrification  and  motion. 

As  Einstein  himself  expresses  it : 

It  is  evident  that  it  is  not  possible  to  attribute  an 
absolute  sense  to  the  notion  of  acceleration,  no  more  than 
to  the  notion  of  velocity.  It  is  only  possible  to  speak  of 
the  acceleration  of  a  material  point  in  connection  with  a 
body  taken  as  the  body  of  reference.  It  follows  from  this 
that  there  is  no  sense  in  attributing  to  a  body  a  "  resist- 
ance to  acceleration  "  in  the  absolute  sense,  like  the  resist- 
ance of  inertia  in  the  classical  mechanics.  Further,  this 
resistance  of  inertia  ought  to  be  so  much  the  greater 
when  there  is,  in  the  neighborhood  of  the  body,  more 
inert  masses  not  in  accelerated  movement.  On  the  other 
hand,  this  resistance  ought  to  disappear  when  these 
masses  participate  in  the  acceleration  of  the  body. 

"  Now  it  is  altogether  remarkable  that  the  equations 


DEMATERIALIZING  MATTER  97 

of  the  gravitational  field  contain  these  different  aspects 
of  the  resistance  of  inertia,  which  one  might  call  the 
relativity  of  inertia. 

The  progress  of  science  is  continually  toward  a  de- 
materialization  of  matter.  Physical  analysis  resolves 
the  crude,  heavy,  solid  stuff  that  our  senses  show  us 
into  finer  and  finer  particles  farther  and  farther  apart 
until  these  practically  disappear  into  mere  points  of 
irradiating  influence.  First  the  mass  is  divided  into 
the  molecule  and  this  again  into  the  atom,  assumed,  at 
the  time  it  was  invented,  to  be  the  ultimate  unit  of 
matter.  But  recently  the  atom  has  been  shown  to  be  a 
sort  of  solar  system,  but  more  complex,  composed  of 
hundreds  of  electrons,  corpuscles  of  electricity,  whose 
radius  is  calculated  to  be  1/10,000,000,000,000  of  a 

centimeter  (a  centimeter  is  so  long).  "But 

the  size  of  the  centers  of  disturbance,  which  in  Ein- 
stein's theory  are  associated  with  matter,  bears  to  the 
size  of  the  electron  about  the  same  proportion  as  the 
size  of  the  smallest  particle  visible  under  the  most 
powerful  microscope  to  that  of  the  earth  itself."  * 

The  old  axiom  was,  "  matter  cannot  act  where  it  is 
not."  The  new  version  might  rather  read :  "  matter 
cannot  act  except  where  it  is  not."  That  is  to  say,  at- 

*  Sir  Joseph  Thomson  in  Nature,  December  4,  1919. 


98  EASY  LESSONS  IN  EINSTEIN 

tention  is  now  directed  to  the  space  surrounding  a 
material  body  or  electrical  corpuscle. 

Although  we  laymen  are  not  concerned  with  the 
niceties  of  astronomical  measurements  there  is  an 
aspect  of  this  conflict  of  theories  that  does  interest 
us.  The  theory  of  Newton  or,  to  go  back  further,  of 
Galileo,  that  the  earth  moves  around  the  sun,  altered 
profoundly  the  philosophical  and  religious  beliefs  of 
the  world,  and  the  theory  of  Einstein  is  much  more 
far-reaching  and  revolutionary  in  its  metaphysical  im- 
plications than  the  former.  Professor  Planck,  who 
has  just  received  the  Nobel  Prize  for  his  discoveries 
in  physics,  said  of  Einstein's  first  paper : 

It  surpasses  in  boldness  everything  previously  sug- 
gested in  speculative  natural  philosophy  and  even  in  the 
philosophical  theories  of  knowledge.  Non-Euclidean 
geometry  is  child's  play  in  comparison.  .  .  .  The  revo- 
lution introduced  into  the  physical  conceptions  of  the 
world  is  only  to  be  compared  in  extent  and  depth  with 
that  brought  about  by  the  Copernican  system  of  the 
universe. 

MUTABLE  THEORIES   AND   STABLE   FACTS 

There  is  a  feeling  very  prevalent  among  the  gen- 
eral public  interested  in  such  things  that  the  founda- 
tions of  modern  science  are  being  swept  away  by  the 
Decent  discoveries.    The  layman  has  been  led  to  believe 


MUTABLE  THEORIES  AND  STABLE  FACTS  99 

that  such  laws  as  gravitation,  the  conservation  of 
matter  and  the  immutability  of  the  elements  are  the 
most  certain  and  absolute  truths  of  science.  But  now 
he  hears  reputable  men  of  science  talk  calmly  about 
the  decay  of  matter  and  the  transformation  of  one  ele- 
ment into  another,  and  gravely  consider  a  theory  which 
makes  invalid  Newton's  three  laws  of  motion.  It  sur- 
prises, even  shocks,  him,  as  much  as  it  would  to  have 
a  convention  of  bishops  discuss  the  question  of  whether 
there  is  a  God,  or  the  Supreme  Court  agree  to  set 
aside  the  Constitution  of  the  United  States,  or  a  con- 
gress of  physicians  resolve  that  all  medicine  does  more 
harm  than  good.  He  knows  that  the  mere  broaching 
of  such  heretical  views  in  these  assemblies  would  be 
met  with  a  storm  of  indignation  and  that  all  the 
weapons  of  contempt,  ridicule  and  even  personal  spite 
would  be  directed  against  the  rash  innovator.  There- 
fore he  is  astonished  and  puzzled  to  see  that  in  the 
scientific  world  these  revolutionary  theories  are  re- 
ceived with  interest  and  even  pleasure,  and  in  the  criti- 
cism to  which  they  are  subjected  there  is  scarcely  a 
trace  of  animosity.  And  he  does  not  see  why  men 
of  science  who  have  accepted  doctrines  apparently 
contradictory  to  their  former  teachings  do  not  appear 
shamefaced  and  apologetic  before  the  public,  like 
augurs  whose  tricks  had  been  exposed. 


100          EASY  LESSONS  IN  EINSTEIN 

The  difficulty  of  the  layman  arises  from  his  not 
understanding  how  a  scientist  looks  at  his  science ;  not 
realizing  how  firmly  he  holds  to  its  facts  and  how 
loosely  he  holds  to  its  theories.  The  scientist  never 
bothers  his  head  with  the  question  whether  a  particu- 
lar theory  is  true  or  false.  He  considers  it  simply  as 
more  or  less  useful,  more  or  less  adequate,  succinct  and 
comprehensive.  A  theory  is  merely  a  tool,  and  he 
drops  one  theory  and  picks  up  another  at  will  and 
without  a  thought  of  inconsistency,  just  as  a  car- 
penter drops  his  saw  and  picks  up  his  chisel.  He  will 
say  that  the  earth  moves  around  the  sun  one  moment, 
and  the  next  will  revert  to  the  theory  of  Chaldean 
astronomers,  because  it  is  more  convenient,  and  say 
"  the  sun  rises." 

Really,  the  new  discoveries  are  not  so  upsetting  to 
science  as  they  appear  to  the  general  public.  Unex- 
pected and  revolutionary  as  they  are,  no  page  of  mil- 
lions that  record  the  experiments  and  observations  of 
science  is  invalidated.  No  man's  work  is  proved 
wrong.  Revolutions  in  science  do  not  destroy;  they 
extend. 

In  the  reaction  of  public  opinion  toward  any  novel 
and  revolutionary  idea  there  are  three  stages  observ- 
able. 

I.  That  it  is  not  true. 


THE  OPPOSITION  TO  NEW  IDEAS     101 

2.  That  it  is  not  new  even  if  it  is  true. 

3.  That  it  does  not  make  any  difference  anyhow. 

The  first  is  merely  the  natural  and  instinctive  re- 
action against  any  disturbing  intellectual  innovation. 
It  is  a  flat  denial  inspired  by  that  unconscious  neopho- 
bia  or  xenophobia  that  possesses  all  of  us  more  or  less. 
The  second  stage  is  the  effort  at  compromise  in  which 
usually  both  the  advocates  and  opponents  of  the  new 
idea  cooperate  by  endeavoring  to  prove  that  it  is  not 
so  novel  and  unprecedented  as  was  at  first  assumed 
but  fits  in  very  fairly  with  our  accepted  notions,  in  fact 
may  be  regarded  as  a  supplement  or  even  a  natural 
development  of  them.  The  third  stage,  like  the  second, 
is  designed  as  an  attempt  to  disarm  opposition  by  allay- 
ing alarm  in  the  conservative  mind. 

The  second  line  of  argument  has  a  good  deal  of 
validity,  for  even  the  most  startling  and  original  idea 
will  be  found  on  closer  examination  to  have  its  roots 
deep  in  the  ground  of  the  past  and  to  have  been  ap- 
proximately anticipated  many  times  before.  The  third 
line  of  argument  also  contains  some  truth  for  we  find 
everyday  life  does  go  on  in  much  the  same  way,  al- 
though it  may  seem  that  the  foundations  have  been 
knocked  from  under  our  mental,  moral  or  social  uni- 
verse by  some  new  notion.  Yet  as  the  popular  mind 
gradually  accepts  and  adapts  itself  to  the  novel  con- 


102          EASY  LESSONS  IN  EINSTEIN 

ception  we  generally  find  that  its  influence  is  even  more 
far-reaching  than  was  at  first  anticipated. 

In  the  case  of  the  Copernican  theory  it  took  about 
two  centuries  for  the  controversy  to  pass  through  the 
three  stages  and  the  mind  of  the  public  to  become  re- 
adjusted to  the  new  conception  of  the  earth's  revolu- 
tion. In  the  case  of  the  Darwinian  theory  of  evolution 
the  process  was  accomplished  in  about  fifty  years.  The 
Einstein  theory  is  more  subversive  of  ordinary  ideas 
than  either  of  the  others  so  it  would  naturally  take 
longer  to  soak  in.  But  the  modern  mind  seems  to  be 
subject  to  acceleration  and  we  see  in  the  two  months 
since  the  notion  has  been  sprung  upon  the  public  that 
all  three  of  the  lines  of  argument  are  appearing  at 
once  and  so  the  controversial  period  may  run  its  course 
in  five  years  though  it  will  be  longer  before  its  indirect 
influence  upon  our  fundamental  philosophy  and  habits 
of  thought  are  fully  felt. 


SCIENTIFIC  VERSUS  LEGAL  LAWS 

In  all  such  discussions  we  must  bear  in  mind  that 
"  law  "  in  the  scientific  sense  of  the  word  means,  not  a 
commandment  or  a  rule,  but  merely  a  way  of  working. 
It  is  a  concise  description  of  how  things  behave.  There 
are  no  laws  in  Nature;  there  are  only  laws  of  Nature; 


SCIENTIFIC  VS.  LEGAL  LAWS          103 

that  is  to  say,  laws  drawn  out  of  Nature  (or,  if  you 
prefer  Latin  to  Anglo-Saxon,  laws  deduced  from 
Nature)  by  man  for  his  own  convenience  in  thinking. 
Physical  laws  are  therefore  essentially  psychological; 
mere  memory  schemes,  calculating  machines.  The  law 
of  gravitation  is  no  more  gravity  than  the  funny 
wriggles  that  my  stenographer  is  making  in  her  note- 
book are  the  sounds  I  am  uttering.  To  change  geome- 
tries does  not  require  any  such  effort  as  to  change  cars. 
It  means  merely  changing  our  minds.  But  this  is 
harder  for  some  of  us  than  it  ought  to  be.  Here  is 
where  the  theory  of  relativity  will  be  of  use  to  us. 
Poincare,  the  French  mathematician,  cousin  of  the 
late  President,  said :  "  These  two  propositions,  '  the 
earth  turns  round '  and  *  it  is  more  convenient  to  sup- 
pose the  earth  turns  round'  have  the  same  meaning. 
There  is  nothing  more  in  the  one  than  in  the  other." 
If  Galileo  and  his  inquisitors  had  understood  the  Prin- 
ciple of  Relativity  it  might  have  saved  them  both 
trouble;  the  former  temporary  imprisonment  and  the 
latter  everlasting  disgrace.  A  revolution  in  science  is 
simply  a  change  in  mental  attitude.  Maybe  a  political 
revolution  is  no  more. 

It  is  disconcerting  to  the  layman  to  be  told,  first, 
that  matter  consists  of  solid  round  atoms  in  empty 
space;  next,  that  it  is  made  of  mere  particles  of  elec- 


104  EASY  LESSONS  IN  EINSTEIN 

tricity  and  negative  at  that ;  then  that  it  is  constituted 
out  of  strains  in  the  ether;  again,  that  the  atoms  are 
bubbles  in  the  ether;  and  finally,  that  there  is  not  any 
ether.  But  these  various  hypotheses  are  like  the  crayon 
strokes  that  an  artist  makes  about  a  figure  he  is  trying 
to  draw.  They  are  all  attempts  at  preliminary  sketches 
for  mental  pictures  of  natural  phenomena.  We  do  not 
call  the  geographers  inconsistent  and  contradictory  be- 
cause one  colors  Massachusetts  red  on  the  map  and  an- 
other colors  it  green.  All  scientific  hypotheses  are  put 
to  the  pragmatic  test  of  which  works  the  best  in  un- 
locking the  secrets  of  Nature.  Is  "wheat"  or 
"  sesame  "  the  magic  word  ?  Whether  we  call  a  dog 
"  Fido  "  or  "  Towser  "  depends  not  on  which  name  is 
shorter  or  sounds  better  but  on  which  the  dog  answers 
to.  If  gravitation  comes  to  heel  better  when  we  say 
"  Einstein  "  than  when  we  say  "  Newton/'  all  right, 
well  change.  I  trust  that  these  frivolous  illustrations 
will  not  lead  my  readers  to  accuse  me  of  treating 
gravity  with  levity. 

The  layman — and  with  him  must  be  included  all 
those  who  have  merely  learned  science  but  not  used  it — • 
talks  a  great  deal  about  "  the  laws  of  Nature,"  which 
he  regards  as  abstract,  immutable,  universal  and  eter- 
nal edicts,  part  of  which  are  transcribed  into  the  text- 
books. To  the  working  scientist  they  are  only  more  or 


SCIENTIFIC  VS.  LEGAL  LAWS          105 

less  convenient  formulas ;  in  the  ultimate  analysis  only 
mnemonic  symbols  for  stringing  together  facts  to  make 
them  easier  to  handle,  like  vibgyor,  for  the  spectrum 
colors.  He  knows  that  most  of  them  are  limited  in 
their  scope  and  only  approximate  in  their  accuracy. 
His  chief  delight  is  in  discovering  these  limitations  and 
irregularities.  He  regards  these  "  laws  "  with  no  awe 
or  reverence.  He  has  no  attachment  for  any  of  them 
—unless  it  happens  to  be  one  that  he  has  formulated 
himself.  If  he  finds  a  new  hypothesis  that  works 
better  he  throws  the  old  one  aside  as  he  does  his  old 
model  dynamo,  or  keeps  it  around  as  handy  still  for 
doing  some  of  the  common  work  of  the  laboratory.  It 
is,  to  recur  to  our  example,  just  as  "  true,"  using  the 
word  in  its  ordinary  sense,  to  say  that  the  sun  goes 
around  the  earth  as  to  say  that  the  earth  goes  around 
the  sun,  for  all  motion  is  relative,  and  we  can  regard 
either  body  as  the  stationary  one  or  both  as  moving, 
as  we  choose.  When  we  say  that  the  statement  that  the 
earth  moves  around  the  sun  is  the  "  true "  one,  we 
merely  mean  that  it  is  the  more  convenient  form  of 
expression,  for  on  this  hypothesis  the  paths  of  the 
earth  and  the  other  planets  become  circles  (or  more 
accurately  speaking,  irregular  and  eccentric  spirals) 
while  on  the  other  and  older  hypothesis  their  paths  are 
very  complicated  and  difficult  to  handle  mathemati- 


106          EASY  LESSONS  IN  EINSTEIN 

cally.  The  theory  that  the  earth  moves  is  not  only 
simpler  than  that  of  a  stationary  earth,  but  it  is  wider 
in  its  scope.  It  explains  more,  that  is,  it  connects  up 
with  other  knowledge,  such  as  the  flattening  at  the 
poles.  Copernicus,  then,  did  not  discover  a  new  fact 
about  the  solar  system.  He  only  invented  a  lazier  way 
of  thinking  about  it. 

The  man  of  science  invents  an  hypothesis  whenever 
he  needs  one  in  his  business.  It  is  to  him  merely  a 
new  tool,  a  novum  organum.  If  there  is  not  an  ether 
it  would  be  necessary  to  create  one.  So  he  did  it.  He 
had  to  have  a  noun  for  the  verb  "  undulate."  When 
he  had  created  it  he  saw  it  was  not  good.  The  prop- 
erties with  which  he  endowed  it  were  self -contradic- 
tory, and  it  refused  either  to  move  with  the  earth  or 
to  pass  through  it.  But  these  theoretical  inconsis- 
tencies do  not  bother  the  physicist  much.  In  spite  of 
them  the  ether  is  a  handy  thing  to  have  about  the 
laboratory.  The  scientist  does  not  abandon  a  theory 
because  it  has  inconsistencies  any  more  than  he  di- 
vorces his  wife  because  she  has  inconsistencies.  Cer- 
tainly the  physicist  did  not  consider  himself  presump- 
tuous in  thus  inventing  ether  for  his  own  convenience. 
He  knew  that  the  ordinary  man  had  in  the  same  way 
invented  "  matter  "  long  ago  for  his  own  convenience. 
It  is  a  crude,  inadequate  and  impossible  idea,  this  naive 


SCIENTIFIC  VS.  LEGAL  LAWS          107 

conception  of  matter  as  something  solid,  heavy,  hard, 
inert,  indestructible,  impenetrable,  colored  and  sur- 
faced; but  it  is  good  enough  for  part  of  the  people 
all  of  the  time  and  for  all  of  the  people  part  of  the 
time.  The  physicist  himself  uses  it  for  everyday. 
Only  in  his  rigorous  moments  does  he  come  down  to 
bed-rock  and  say,  with  Poincare,  "  Mass  is  a  co-efficient 
which  it  is  convenient  to  introduce  into  calculations." 

But  when  the  physicist  thus  reduces  matter  to  a  small 
italic  m  some  people  are  sure  to  say  that  he  is  denying 
the  existence  of  ma'tter.  What  would  they  say  about 
Riemann  who  considers  matter  to  be  holes  in  the  ether? 
A  definition  is  a  different  thing  from  a  denial.  There 
are  people  among  us  who  deny  the  existence  of  matter 
and  they  call  themselves  "  Scientists,"  too,  but  they  are 
not  the  ones  who  are  devoting  their  days  and  nights  to 
the  study  of  the  workings  of  matter  in  order  to  make 
it  the  servant  of  man. 

A  professor  of  chemistry  would  not  think  of  asking 
his  students  if  the  atomic  theory  is  true  any  more  than 
he  would  ask  them  if  the  atomic  theory  is  blue.  He 
does  not  care  whether  they  believe  the  atomic  theory 
or  not.  He  only  wants  them  to  be  able  to  use  the 
atomic  theory  for  getting  certain  valuable  results. 
Consequently,  he  watches  with  interest  and  without  ap- 
prehension the  progress  of  discovery  in  radio-activity 


108          EASY  LESSONS  IN  EINSTEIN 

which  is  undermining  the  old  conception  of  the  atom. 
He  would  be  glad  to  get  rid  of  the  atomic  theory  if  he 
could  find  something  better  because  after  all  it  is  a 
clumsy  thing  and  will  not  hold  half  the  facts  he  wants 
to  put  into  it.  He  would  have  no  more  hesitation 
about  dropping  it  than  he  has  in  setting  down  one 
beaker  to  pick  up  a  larger  one  when  what  he  has  in  the 
first  is  frothing  over.  He  does  not  want  to  spill  any- 
thing, but  he  does  not  care  what  vessel  it  is  in.  Revolu- 
tions in  science  never  go  backward  and  they  differ 
from  political  revolutions  in  that  nothing  worth  saving 
is  lost  in  transition.  The  new  theory  must  always  in- 
clude all  that  the  old  one  does  and  more.  In  their 
struggle  for  existence,  formulas  fight  like  snakes;  the 
one  that  can  swallow  the  other  beats.  Now  a  four- 
dimensional  universe  can  take  in  a  three-dimensional 
universe  and  have  space  to  spare  for  whatever  the  nar- 
rower conception  could  not  include  so  it  seems  likely 
to  prevail. 

We  now  know  how  to  sympathize  with  those  poor 
frightened  people  who  lived  in  the  times  of  Copernicus 
and  Galileo  when  they  were  told  that  the  solid  earth 
on  which  they  stood  was  not  supported  by  anything, 
but  whirling  about  and  rushing  around  through  empty 
space  and  that  half  the  time  they  hung  with  their  heads 
down  over  immeasurable  space  with  nothing  to  hold  on 


TIME,  SPACE,  AND  GRAVITATION      109 

to.    But  they  got  used  to  it  in  time  and  lived  happily 
ever  after.    So  may  we. 

For  the  benefit  of  those  who  want  to  get  their  in- 
formation at  first  hand  I  append  an  article  by  Dr. 
Einstein  himself  which  appeared  in  the  London  Times 
of  December  13,  1919,  and  in  Science  of  January  6, 
1920: 

TIME,  SPACE,  AND  GRAVITATION 
By  Dr.  Albert  Einstein 

I  respond  with  pleasure  to  your  Correspondent's  re- 
quest that  I  should  write  something  for  the  Times  on  the 
Theory  of  Relativity. 

After  the  lamentable  breach  in  the  former  interna- 
tional relations  existing  among  men  of  science,  it  is  with 
joy  and  gratefulness  that  I  accept  this  opportunity  of 
communication  with  English  astronomers  and  physicists. 
It  was  in  accordance  with  ttie  high  and  proud  tradition 
of  English  science  that  English  scientific  men  should  have 
given  their  time  and  labor,  and  that  English  institutions 
should  have  provided  the  material  means,  to  test  a  theory 
that  had  been  completed  and  published  in  the  country  of 
their  enemies,  in  the  midst  of  war.  Although  investiga- 
tion of  the  influence  of  the  solar  gravitational  field  on 
rays  of  light  is  a  purely  objective  matter,  I  am  none 
the  less  very  glad  to  express  my  personal  thanks  to  my 
English  colleagues  in  this  branch  of  science ;  for  without 
their  aid  I  should  not  have  obtained  proof  of  the  most 
vital  deduction  from  my  theory. 


110          EASY  LESSONS  IN  EINSTEIN 

There  are  several  kinds  of  theory  in  Physics.  Most 
of  them  are  constructive.  These  attempt  to  build  a 
picture  of  complex  phenomena  out  of  some  relatively 
simple  proposition.  The  kinetic  theory  of  gases,  for 
instance,  attempts  to  refer  to  molecular  movement  the 
mechanical,  thermal,  and  diffusional  properties  of  gases. 
When  we  say  that  we  understand  a  group  of  natural 
phenomena,  we  mean  that  we  have  found  a  constructive 
theory  which  embraces  them. 

But  in  addition  to  this  most  weighty  group  of  theories, 
there  is  another  group  consisting  of  what  I  call  theories 
of  principle.  These  employ  the  analytic,  not  the  synthetic 
method.  Their  starting-point  and  foundation  are  not 
hypothetical  constituents,  but  empirically  observed  gen- 
eral properties  of  phenomena,  principles  from  which 
mathematical  formulae  are  deduced  of  such  a  kind  that 
they  apply  to  every  case  which  presents  itself.  Thermo- 
dynamics, for  instance,  starting  from  the  fact  that  per- 
petual motion  never  occurs  in  ordinary  experience,  at- 
tempts to  deduce  from  this,  by  analytic  processes,  a 
theory  which  will  apply  in  every  case.  The  merit  of 
constructive  theories  in  their  comprehensiveness,  adapta- 
bility, and  clarity,  that  of  the  theories  of  principle,  their 
logical  perfection,  and  the  security  of  their  foundation. 

The  theory  of  relativity  is  a  theory  of  principle.  To 
understand  it,  the  principles  on  which  it  rests  must  be 
grasped.  But  before  stating  these  it  is  necessary  to  point 
out  that  the  theory  of  relativity  is  like  a  house  with  two 
separate  stories,  the  special  relativity  theory  and  the  gen- 
eral theory  of  relativity. 

Since  the  time  of  the  ancient  Greeks  it  has  been  well 
known  that  in  describing  the  motion  of  a  body  we  must 
refer  to  another  body.  The  motion  of  a  railway  train  is 


TIME,  SPACE,  AND  GRAVITATION     111 

described  with  reference  to  the  ground,  of  a  planet  with 
reference  to  the  total  assemblage  of  visible  fixed  stars. 
In  physics  the  bodies  to  which  motions  are  spatially  re- 
ferred are  termed  systems  of  coordinates.  The  laws  of 
mechanics  of  Galileo  and  Newton  can  be  formulated  only 
by  using  a  system  of  coordinates. 

The  state  of  motion  of  a  system  of  coordinates  cannot 
be  chosen  arbitrarily  if  the  laws  of  mechanics  are  to  hold 
good  (it  must  be  free  from  twisting  and  from  accelera- 
tion). The  system  of  coordinates  employed  in  mechanics 
is  called  an  inertia-system.  The  state  of  motion  of  an 
inertia-system,  so  far  as  mechanics  are  concerned,  is  not 
restricted  by  nature  to  one  condition.  The  condition  in 
the  following  proposition  suffices :  a  system  of  coordinates 
moving  in  the  same  direction  and  at  the  same  rate  as  a 
system  of  inertia  is  itself  a  system  of  inertia.  The  special 
relativity  theory  is  therefore  the  application  of  the  follow- 
ing proposition  to  any  natural  process : — "  Every  law  of 
nature  which  holds  good  with  respect  to  a  coordinate 
system  K  must  also  hold  good  for  any  other  system  K', 
provided  that  K  and  K'  are  in  uniform  movement  of 
translation. 

The  second  principle  on  which  the  special  relativity 
theory  rests  is  that  of  the  constancy  of  the  velocity  of 
light  in  a  vacuum.  Light  in  a  vacuum  has  a  definite  and 
constant  velocity,  independent  of  the  velocity  of  its 
source.  Physicists  owe  their  confidence  in  this  proposi- 
tion to  the  Maxwell-Lorentz  theory  of  electro-dynamics. 

The  two  principles  which  I  have  mentioned  have  re- 
ceived strong  experimental  confirmation,  but  do  not  seem 
to  be  logically  compatible.  The  special  relativity  theory 
achieved  their  logical  reconciliation  by  making  a  change 
in  kinematics,  that  is  to  say,  in  the  doctrine  of  the  physi- 


112          EASY  LESSONS  IN  EINSTEIN 

cal  laws  of  space  and  time.  It  became  evident  that  a 
statement  of  the  coincidence  of  two  events  could  have  a 
meaning  only  in  connection  with  a  system  of  coordinates, 
that  the  mass  of  bodies  and  the  rate  of  movement  of 
clocks  must  depend  on  their  state  of  motion  with  regard 
to  the  coordinates. 

But  the  older  physics,  including  the  laws  of  motion 
of  Galileo  and  Newton,  clashed  with  the  relativistic  kine- 
matics that  I  have  indicated.  The  latter  gave  origin  to 
certain  generalized  mathematical  conditions  with  which 
the  laws  of  nature  would  have  to  conform  if  the  two 
fundamental  principles  were  compatible.  Physics  had 
to  be  modified.  The  most  notable  change  was  a  new  law 
of  motion  for  (very  rapidly)  moving  mass-points,  and 
this  soon  came  to  be  verified  in  the  case  of  electrically- 
laden  particles.  The  most  important  result  of  the  special 
relativity  system  concerned  the  inert  mass  of  a  material 
system.  It  became  evident  that  the  inertia  of  such 
a  system  must  depend  on  its  energy-content,  so  that  we 
were  driven  to  the  conception  that  inert  mass  was  noth- 
ing else  than  latent  energy.  The  doctrine  of  the  con- 
servation of  mass  lost  its  independence  and  beqame 
merged  in  the  doctrine  of  conservation  of  energy. 

The  special  relativity  theory,  which  was  simply  a  sys- 
tematic extension  of  the  electro-dynamics  of  Maxwell 
and  Lorentz,  had  consequences  which  reached  beyond 
itself.  Must  the  independence  of  physical  laws  with  re- 
gard to  a  system  of  coordinates  be  limited  to  systems  of 
coordinates  in  uniform  movement  of  translation  with 
regard  to  one  another  ?  What  has  nature  to  do  with  the 
coordinate  systems  that  we  propose  and  with  their  mo- 
tions? Although  it  may  be  necessary  for  our  descrip- 
tions of  nature  to  employ  systems  of  coordinates  that 


TIME,  SPACE,  AND  GRAVITATION     113 

we  have  selected  arbitrarily,  the  choice  should  not  be 
limited  in  any  way  so  far  as  their  state  of  motion  is 
concerned.  (General  theory  of  relativity.)  The  appli- 
cation of  this  general  theory  of  relativity  was  found  to  be 
in  conflict  with  a  well-known  experiment,  according  to 
which  it  appeared  that  the  weight  and  the  inertia  of  a 
body  depended  on  the  same  constants  (identity  of  inert 
and  heavy  masses).  Consider  the  case  of  a  system  of 
coordinates  which  is  conceived  as  being  in  stable  rotation 
relative  to  a  system  of  inertia  in  the  Newtonian  sense. 
The  forces  which,  relatively  to  this  system,  are  cen- 
trifugal must,  in  the  Newtonian  sense,  be  attributed  to 
inertia.  But  these  centrifugal  forces  are,  like  gravitation, 
proportional  to  the  mass  of  the  bodies.  Is  it  not,  then, 
possible  to  regard  the  system  of  coordinates  as  at  rest, 
and  the  centrifugal  forces  as  gravitational?  The  inter- 
pretation seemed  obvious,  but  classical  mechanics  for- 
bade it. 

This  slight  sketch  indicates  how  a  generalized  theory 
of  relativity  must  include  the  laws  of  gravitation,  and 
actual  pursuit  of  the  conception  has  justified  the  hope. 
But  the  way  was  harder  than  was  expected,  because  it 
contradicted  Euclidean  geometry.  In  other  words,  the 
laws  according  to  which  material  bodies  are  arranged  in 
space  do  not  exactly  agree  with  the  laws  of  space  pre- 
scribed by  the  Euclidean  geometry  of  solids.  This  is 
what  is  meant  by  the  phrase  "  a  warp  in  space."  The 
fundamental  concepts  "straight,"  "plane,"  etc.,  accord- 
ingly lose  their  exact  meaning  in  physics. 

In  the  generalized  theory  of  relativity,  the  doctrine  of 
space  and  time,  kinematics,  is  no  longer  one  of  the  abso- 
lute foundations  of  general  physics.  The  geometrical 
states  of  bodies  and  the  rates  of  clocks  depend  in  the 


EASY  LESSONS  IN  EINSTEIN 

first  place  on  their  gravitational  fields,  which  again  are 
produced  by  the  material  systems  concerned. 

Thus  the  new  theory  of  gravitation  diverges  widely 
from  that  of  Newton  with  respect  to  its  basal  principle. 
But  in  practical  application  the  two  agree  so  closely  that 
it  has  been  difficult  to  find  cases  in  which  the  actual  dif- 
ferences could  be  subjected  to  observation.  As  yet  only 
the  following  have  been  suggested : — 

1.  The  distortion  of  the  oval  orbits  of  planets  round 
the  sun  (confirmed  in  the  case  of  the  planet  Mercury). 

2.  The  deviation  of  light-rays  in  a  gravitational  field 
(confirmed  by  the  English  Solar  Eclipse  expedition). 

3.  The  shifting  of  spectral  lines  toward  the  red  end  of 
the  spectrum  in  the  case  of  light  coming  to  us  from  stars 
of  appreciable  mass  (not  yet  confirmed). 

The  great  attraction  of  the  theory  is  its  logical  consis- 
tency. If  any  deduction  from  it  should  prove  untenable, 
it  must  be  given  up.  A  modification  of  it  seems  im- 
possible without  destruction  of  the  whole. 

No  one  must  think  that  Newton's  great  creation  can 
be  overthrown  in  any  real  sense  by  this  or  by  any  other 
theory.  His  clear  and  wide  ideas  will  forever  retain  their 
significance  as  the  foundation  on  which  our  modern  con- 
ceptions of  physics  have  been  built. 

A  final  comment.  The  description  of  me  and  my  cir- 
cumstances in  The  Times  shows  an  amusing  feat  of  im- 
agination on  the  part  of  the  writer.  By  an  application  of 
the  theory  of  relativity  to  the  taste  of  readers,  today  in 
Germany  I  am  called  a  German  man  of  science,  and  in 
England  I  am  represented  as  a  Swiss  Jew.  If  I  come 
to  be  regarded  as  a  bete  noire,  the  descriptions  will  be 
reversed,  and  I  shall  become  a  Swiss  Jew  for  the  Ger- 
mans and  a  German  man  of  science  for  the  English ! 


And  finally 

IF  YOU  WANT  TO  READ  MORE  ABOUT 
THE  EINSTEIN  THEORIES 

For  the  non-mathematical  reader: 
ABBOTT,  EDWIN. 

Flatland,  by  A  Square.    Boston,  1891. 

An  amusing  way  of  leading  up  to  the  fourth  dimension. 

CAMPBELL,  NORMAN. 

The    Commonsense    of    Relativity.     Philosophical   'Maga- 
zine, April,  1911. 
CARR,  WILDON. 

The  Metaphysical   Implications  of  the  Theory  of  Rela- 
tivity.   Philosophical  Review,  Jan.,  1915. 
CARUS,  PAUL. 

The  Principle  of  Relativity.     Chicago:  Open  Court  Pub- 
lishing Co.,  1913. 
COMSTOCK,  D.  F. 

The    Principle    of    Relativity.      Science,    May    20,    1910, 
vol.  31,  p.  767. 
CUNNINGHAM,  E. 

Einstein's     Relativity    Theory    of    Gravitation.     Nature, 
Dec.  4,  n,  and  18,  1919. 

An  interesting  non-mathematical  discussion  of  the  latest 
phases  of  the  theory. 
EDDINGTON,  A.  S. 

Einstein's    Theory    of    Space   and   Time.     Contemporary 
Review,  Dec.,  1919. 

Good  popular  article. 
EDDINGTON,  A.  S. 

Gravitation.    Scientific  American  Supplement,  July  6  and 
13,  1918. 

An  excellent  popular  explanation  by  the  leading  British 
disciple  of  Einstein. 
EINSTEIN,  A. 

Time,    Space,   and   Gravitation.     Science,   Garrison,   1920, 
Jan.  3,  n.s.,  vol.  51,  p.  8-10. 

My  Theory.     Living  Age.    Boston,  1920,  vol.  304,  p.  4i-3» 
Jan.  3. 
FLAMMARION,  CAMILLE. 

Lumen.    New  York:  Dodd,  Mead  and  Co.,  1897. 
Contains   nothing  about   Einstein   but  presents  the   rela- 
tivity of  time  in  fantastic  form. 


116  BIBLIOGRAPHY 

KEYSER,  C.  J. 

Concerning  the  Figure  and  the  Dimensions  of  the  Uni- 
verse of  Space.    Science,  June  13,  1913. 
LODGE,  SIR  OLIVER. 

The  New  Theory  of  Gravity.    Nineteenth  Century,  Dec., 
1919. 

The  Ether  versus  Relativity.     Fortnightly  Review,  Jan., 
1020. 

Admirable  article  by  a  courteous  opponent. 
POINCARE,  HENRI. 

Science  and  Method;  also  contained  in  The  Foundations 
of  Science.    New  York:  The  Science  Press,  1913. 
RUSSELL,  BERTRAND. 

The  Relativity  Theory  of  Gravitation.     English  Review, 
Dec.,  1919. 

A  clear  explanation  by  one  of  the  foremost  of  British 
philosophers. 
THOMSON,  J. 

Deflection    of    Light    by    Gravitation    and    the    Einstein 
Theory  of  Relativity.     Scientific  Monthly,  Garrison,  N.  Y., 
1920,  vol.  10,  p.  79-85,  Jan. 
VARIOUS  WRITERS. 

The  Fourth  Dimension   Simply  Explained.     New  York: 
Munn  and  Co.,  1910. 

The  essays  submitted  for  a  prize  offered  by  the  Scientific 
American.     Twenty-two   mathematicians   try   their   best   to 
justify  the  title  and  if  they  do  not  succeed  it  is  not  their 
fault. 
WETZEL,  REINHARD  A. 

The    New    Relativity   in    Physics.     Science,   New   York, 
1913.    New  sen,  vol.  38,  pp.  466-474. 

Explains  the  relativity  of  time  with  diagrams  and  refer- 
ences to  the  literature. 


Other  articles  of  general  interest  may  be  found  in: 

Science:   July   16,    1009;    May  20,   1910;   June  20,   1913; 
April  24,  1914;  Dec.  5,  1919. 

Scientific  American  Supplement:  April  7,  1917;  Dec.  17, 
1910. 

London  Nation:  Nov.  14  and  Dec  27,  1919. 

London    Times:    Nov.    8,    18,   and    25,    Dec.    4  'and    19, 
1919. 

London  Nature:  Almost  every  number  in  Nov.,  Dec.,  1919, 
Jan.,  Feb.,  1020. 

New  York  Times:  Nov.  7  and  16,  Dec.  21,  1919. 

New  York  Sun:  Nov.  10,  1919. 
The  New  Republic:  Jan.  21,  1920. 


BIBLIOGRAPHY  117 

lFor  the  Mathematical  reader: 
EINSTEIN,  ALBERT. 

Bases  physiques  d'une  theorie  de  la  gravitation.  Societe 
Astronomique  de  France.  Bulletin,  Paris,  1917,  Tome  31, 
pp.  407-411. 

Die  formale  Grundlage  der  allgemeinen  Relativitats- 
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schaften.  Sitzungsberichte,  Berlin,  1904  /(Juli-Dez.),  pp. 
1030-1085. 

Die  Grundlagen  der  allgemeinen.  Relativitatstheorie.  An- 
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1st  die  Tragheit  eines  Korpers  von  seinem  Energieinhalt 
abhangig?  Annalen  der  Physik,  Leipzig,  1905,  Band  18, 
Folge  4,  pp.  639-644. 

Lichtgeschwindigkeit  und  Statik  des  Gravitationsfeldes. 
'Annalen  der  Physik,  Leipzig,  1912,  Band  38,  Folge  4,  pp. 
355-369. 

Prinzipielles  zur  allgemeinen  Relativitatstheorie.  Annalen 
der  Physik,  Leipzig,  1918,  Band  55,  Folge  4,  pp.  241-244. 

Uber  das  Relativitatsprinzip  und  die  aus  demselben 
gezogenen  Folgerungen.  Jahrbuch  der  Radio aktivit'dt  und 
Elektronik,  Leipzig,  1908,  Band  4,  pp.  411-462. 

Uber  den  Einfluss  der  Schwerkraft  auf  die  Ausbreitung 
des  Lichtes.  Annalen  der  Physik,  Lypzig,  1911.  Band  35, 
p.  808-908. 

Uber  die  Moglichkeit  einer  neuen  Priifung  des  Relativi- 
tatsprinzips.  Annalen  der  Physik,  Leipzig,  1907,  Band  23, 
p.  197-208. 

Uber  die  vom  Relativitatsprinzip  geforderte  Tragheit  der 
Energie.  Annalen  der  Physik,  Leipzig,  1907,  Band  23, 
Folge  4,  PP.  371-384. 

Uber  einen  die  Erzeugung  und  Verwandlung  des  Lichtes 
betreffendes  heuristischen  Gesichtspunkt.  Annalen  der 
Physik,  Leipzig,  1905,  Band  17,  Folge  4,  pp.  132-148. 

Zum  gegenwartigen  Stande  des  Gravitationsproblems. 
Physikalische  Zeitschrift,  Leipzig,  1913,  Band  14,  pp.  1249- 
1266. 

Zum  Relativitats  Problem.  Scientia,  Bologna,  1914,  vol. 
15,  PP.  337-48. 

Zur  Elektrodynamik  bewegter  Korper.  Annalen  der 
Physik,  Leipzig,  1905,  Band  17,  Folge  4,  PP-  891-921. 

Zur  Theorie  der  Lichterzeugung  und  Lichtabsorption. 
'Annalen  der  Physik,  Leipzig,  1906,  Band  20,  Folge  4,  pp. 
199-206. 

Spielen    Gravitationsfelder    im    Aufbau    der    materiellen 
Elementarteilchen    eine    wesentliche    Rolle?     Sits.    Preuss. 
Akad.  Wiss.,  April  10,  1919. 
EINSTEIN,  ALBERT,  and  MARCEL  GROSSMAN. 

Entwurf   einer  verallgemeinerten   Relativitatstheorie  und 


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einer  Theorie  der  Gravitation.    ZeitscJTrift  fur  Mathematik 
und  Physik,  Leipzig,  1914,  Band  62,  pp.  225-261. 
EINSTEIN,  LORENTZ  and  MINKOWSKI. 

Relativitatsprinzip,  Das.  Eine  Sammlung  von  Abhand- 
lungen.  Mit  Anmerkungen  von  A.  Sommerfeld  und  Vor- 
wort  von  O.  Blumenthal.  Leipzig:  B.  G.  Teubner,  1913. 
89  p.  (Fortschritte  der  mathematichen  Wissenschaften  in 
Monographien,  Heft.  2.) 
A  reprint  of  these  three  famous  fundamental  papers. 

ABRAHAM,  M. 

Die    neue    Mechanik.     Scientia,   Bologna,    1914,   vol.    15, 
pp.  8-27. 

Nochmals  Relativat  und  Gravitation  Bemerkungen  zu  A. 
Einsteins  Erwiderung.    Annalen  der  Physik,  Leipzig,  1912, 
Folge  4,  vol.  39,  pp.  444-448. 
BACKLUND,  A.  V. 

Zusammenstellung  einer  Theorie  der  klassischen  Dynamik 
und  der  neuen  Gravitationstheorie  von  Einstein.    Arkiv  for 
mathematik,  astronomie,  och  fysik,  Stockholm,  1919,  Band 
14,  no.  n,  64  seite. 
BATEMAN,  H. 

General  Relativity  Theory.     Phil.  Mag.,  Feb.,   1909,  vol. 

37- 

Applies  the  theory  to  life  and  mind. 
BRILLOUIN,  MARCEL. 

Propos   Sceptiques   au    Sujet   du   Principe   de   Relativite. 
Scientia,  Bologna,  1913,  vol.  13,  pp.  10-26. 
BROSE,  HENRY  L. 

Einstein's  Theory  of  Relativity   (non-math,  form).     Lec- 
ture published  in  pamphlet  by  B.  H.  Blackwell.     Noted  in 
English  Mechanic,  Dec.  19,  1919. 
CARMICHAEL,  ROBERT  DANIEL. 

The    Theory    of    Relativity.     Mathematical  Monographs, 
no.  12.    New  York:  John  Wiley,  1913. 
COBB,  CHARLES  W. 

Relativity.    Journal  of  Philosophy,  Psychology,  and  Scien- 
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CONWAY,   A.   W. 

Relativity.    Edin.  Math.  Tracts,  no.  3,  London,  1913. 
CROMMELIN,  A.  C.  D. 

Results  of  the  Total  Solar  Eclipse  of  May  29  and  the 
Relativity  Theory.    Science,  vol.  50,  pp.  518-520.    Sci.  Amer. 
Sup  p.,  Dec.  6,  1919. 
CUNNINGHAM,  E. 

Report  on  the  Relativity  Theory  of  Gravitation.    London, 
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1919,  vol.  26,  pp.  26-34. 
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See   also:    Astro-Physical  Journal,   vol.   37,   pp.    100-193, 
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THANKS 

Most  of  the  mathematical  references  cited  above  have  been 
borrowed  bodily  from  the  book  list  prepared  by  Miss  Mary  E. 
Todd  of  the  Science  Room  of  the  New  York  Public  Library 
and  published  in  the  Library  Journal.  As  soon  as  the  Einstein 
craze  struck  New  York  these  books  were  placed  on  a  long  table 
and  it  has  been  difficult  to  find  a  seat  at  this  table,  day  or 
evening,  ever  since.  At  Cambridge  University  when  Professor 
Eddington  lectured  on  the  Einstein  theory  the  students  waiting 
for  the  opening  of  the  hall  doors  formed  a  cue  extending  half- 
way across  Trinity  Great  Court.  It  is  unusual  in  any  university 
to  have  "  standing  room  only "  at  a  lecture  on  mathematical 
physics. 

About  half  of  the  present  volume  appeared  in  The  Inde- 
pendent of  November  29,  December  7,  13,  and  20,  1919,  and  I 
am  indebted  to  Hamilton  Holt,  the  editor,  and  to  Karl  V.  S. 
Rowland,  the  publisher  of  that  magazine,  for  the  privilege  of 
reprinting  them  in  book  form.  I  am  further  grateful  to  several 
professors  of  physics,  mathematics,  astronomy  and  philosophy 
who  have  been  kind  enough  to  criticize  and  correct  this  ma- 
terial, but  since  it  would  not  be  fair  to  hold  them  responsible 
for  my  personal  views  and  unconventional  language  I  shall  have 
to  express  my  thanks  to  them  in  private. 


INDEX 


Bergson,  Henri,  47,  5*,  52 

Carlyle,  iv 

Curvature  of  space,  26,  35,  38, 
96 

Eclipse  observations,  2,  65,  72 
Einstein,  Albert 

Postulates  of,  13,  83,  HI 

Theory  of  time,  109 

Theory  of  gravitation,  39,  58, 
76,  80,  86,  93,  96,  109 

Life  of,  78 

Works  of,  116,  117 
Equivalence,    principle   of,    14, 

83,86 
Ether,  8,  11,  88,  106 

Flammarion,  Camille,  40 

Flatland,  35,  57 

Fourth  dimension,  24,  34,  49 

Gravitation,  68,  74,  77,  80,  86, 
90 

Laws,  natural,  102,  109 

Light,  deflection  of  ray,  II,  62, 

,    79,  85 

Light,  pressure  of,  07,  93 
Lodge,  Sir  Oliver,  2,  68,  75,  87, 

88 
Lorentz,  22,  HI,  112,  118 

Macdonald,  George,  34 
Maxwell,  Clerk,  67,  in,  112 
Mercury,  orbit  of,  14,  66 


Michelson  and  Morley  experi- 
ment, n,  21,  22,  85 

Minkowski,  iv,  18 

Mirror,  images,  18 

Motion  picture  illustrations,  31, 
44,  46,  50,  53 

Non-Euclidean    geometry,    30, 

48,  57,  112 
Newton,  15,  23,  39,  66,  76,  79, 

87,  90,  95 

Planck,  98,  121 
Poincare,  H.,  88,  107 

Relativity     of     measurements, 

15,  20,  26 

Relativity  of  motion,  4, 8, 15, 23 
Relativity  of  time,  15, 24, 47, 51 

Slade,  58,  60 

Spectrum,  shifting  of  lines  of, 
14,  77,  85 

Theories,  reception  of  new,  98, 

101 

Theory  of  relativity,  2,  15 
Thomson,  Sir  Joseph,  3,  93,  94, 

95 
Time  as  fourth  dimension,  30, 

.    32,  49 
Time,  reversal  of,  41,  44 

Wells,  H.  G.,  32,  34,  40,  52 
Zollner,  58,  60 


123 


T 


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